Upon launching the game with the DLC, there is NOT an option to adjust the difficulty level. It will use the difficulty setting within the current saved game. So if you just completed the main game on "Insanity" difficulty to get the achievement and then attempt the arena DLCs it’s going to be a near-impossible challenge!
I recommend starting out on "Easy" difficulty. To do this, launch the main game. Select "New Game" from the menu and choose the new difficulty. You don’t have to watch the Intro. Just close out of the game at that point. In fact, when I did this, it changed the difficulty without overwriting my saved game. However, just to be cautious:
*Note that this may overwrite any progress in your current saved game! If you want to keep your saved game, make sure to back it up (all files)! The saved game location folder is: My Documents\My Games\Afterfall InSanity\

• At the beginning of each encounter, walk over to the conveyor to pick up your weapon before heading out into the arena. Note that enemies no longer drop weapons so this is the only weapon you may use during the entire encounter.
  
• Auto health regeneration is disabled in the Arena, however, Albert has a generous starting health of 400 for each encounter. You can take a lot of damage and still make it through.
  
• Using the evade roll (direction + double tap space bar) allows Albert to move quickly, avoid damage, and continue to reload a weapon without stopping.
  
• There are no check points. The whole thing has to be done in one play through without dying or you start over at the first encounter.
  
• The last enemy in a wave will kneel to the ground waiting for you to do a finisher. This is not necessary and he will eventually die, unlike in the main story. This is good opportunity to use the extra time to reload and grab some more ammo at a station.
  
• During the mini boss fights, endless enemies will spawn in. These waves can be used to increase your points for the leader board.

10/29/14: I got a request for a video walkthrough/speed-run of the Dirty Arena. Even months later, after creating this guide, no one else has posted one. I just started learning how to use OBS to record videos. So here it is … enjoy!

No choice. It's a decent One Handed Melee with average speed and damage.

• Do not walk outside the rope (globe lights) boundary or gunners will shoot from the buildings.

Pretty straight forward with a few 1-hit-kill mad men.
More 1-hit-kill mad men. Barrels will begin being thrown into the center of the ring. Just be carful to avoid walking into an explosion.
One Solider with Cattle Prod can be taken out with a barrel. Either keep him in the center and wait for a barrel to explode or hit one and quickly evade/run. The solder is followed by a group of normal mad men. Recommend using the barrels on them.
Groups of mad men with swords as well as mutants. Just keep running a circle around the center of the ring until the barrels take them out. The pattern is two barrels thrown and then a flaming barrel. Just be sure to time it so the enemy is in the center and you're running to the side as the flaming barrel is thrown.
Mini boss - large flame soldier. Avoid his lung attack. Better yet, use his lung attack against him - stand next to a barrel, when he is about to attack, hit the barrel and evade. He is fairly weak and can be killed with a few melee attacks or with a single barrel explosion.
Strike the barrel when he is about to leap for an instant kill.

It's a choice between a Monkey Wrench or Power Hammer. I suggest the Power Hammer. It is the superior weapon.

• Try to avoid standing in the center of the ring on this one as gun man will shoot from the buildings. Use the fences directly in front of your starting position end to avoid their line of site. Stay on that side.
  
• Keep an eye out for exploding fire flies. If one is coming at you, run in an adjacent direction. These are the biggest threat in this encounter. When the spot you, they turn red and turn into a projectile. You can use them as a weapon this way as they can take out a whole group of enemies.

With the power hammer, the few mad men should be 1 hit kills followed by a gun man. Use evade rolls to get close enough to the gun men to take them out without getting shot.
More one hit kill men. Pretty straight forward - avoid the center of the ring.
One hit kill Mutants, followed by mad men, and finally a gun man. Let them come to you.
More mad men, followed by a gun man.
A Large sumo mutant and regular mutant. A trick is to run to the cable on the side of the building and wait for them get them into the center. Then hit the cable to release a cargo container on top of them. If it misses, there are flames that shoot out in the corner of the arena where you can lure them to.
When he crouches on the ground, hit the cable and the cargo container and it's barrels will kill him.

You are given the automatic shotgun. This is the only time the ammo station is not available at the starting area.
The same first boss from the main story line. Kill any of his mad men that come after you. There are two ammo refill stations on either side of the arena. Head for one from the start since you will need plenty of it.
Wait behind a fence for the throwing shield attack. While he is retrieving the shield, fire at the target on his belly. Do this about 3 times.
He will switch from a whip to hammer weapon. Try to run around a fence and get him stuck behind a flaming barrel. Shoot the target on his chest. If he happens to hit you, try evading toward him (counter-intuitive) to get back up and away without taking much damage.

If you find it hard to get distance between you, try using an evade move while reloading to get ahead. Since you cannot run while reloading this is faster than walking.

A choice between pistol and semi-automatic. I recommend the pistol as it is easier to aim and does more damage.
Don't forget to hit up the ammo refill station before starting.
There's a couple of gun men and mad men. A nice area to pick them off is the platform at the end of the arena and refill in between rounds. Watch out for a possible gunmen on the adjacent balcony. From here you can take your time and sniper without being shot at be enemies on the building:
This is the best spot for sniping enemies. Just keep looking here and picking them off. If none come out, try running over to the other side.
Rinse and repeat.
Again, if you are using the pistol and taking time to aim you should have enough bullets to finish them off and only refill at the closest ammo station between waves.
Mutants and gun men spawn in. Let them fight each other and pick off any that remain from the platform.
Mini boss - bounty hunter soldier gun man and a few normal gun man. They can all be sniped from the platform. The bounty hunter will take a few rounds, but there should be enough ammo if you refilled between waves. A Barrel will also kill him quickly.

A choice between shotgun or automatic shotgun. I'd go for the automatic for longer range. Don't forget to hit up the ammo station before starting.
A mix of mad men and gun men. If you chose the automatic, the sniping platform mentioned in the previous encounter can be used here.
They thrown in some flames and stuff, but if you're sniping from the platform it's not any different.
More sniping. There are exploding barrels thrown in the center, but the it's all avoided here.
Camp it out.
Mutants and a cattle prod mini boss. Not much different. Just lure them up the ramp of the platform and pick them off from above. Sometimes there isn't even a fight, he just walks into a flame and dies within the first few seconds.

No choice - the semi-automatic. Load up on ammo before heading out.
Surprise, surprise ... It's the same second boss that was in the main story, but this time it's a little easier as you can do damage to the boss without hitting a specific area. In the first part he is invincible so don't attempt to attack him. Pick off the body guards (cattle prodders) and be careful not to explode any barrels ... save these for when the boss reappears and it will be super easy. Dodge any cars that are thrown toward you (there's a blinding light before it happens.) Also avoid stepping into the light circles that form on the floor.

The boss will reappear and switch his attack to a focused earth quake twice in a row. Dodge these attacks using evade moves and shoot in between. If he is near a barrel, blow it up for an instant kill. Otherwise, continue to shoot him a few times and he will eventually die.

*If you run out of ammo (this happened to me once), keep dodging his attacks and try to lour him into the shocking circles. He will take shock damage and die.

When he reappears it's usually here. Just shoot the barrel and you're done.

Choice between semi-automatic or machine gun. I always choose the bigger gun myself.
The sniping platform is open. Guess what? I suggest making it easy on yourself and do some camping. There are spiny death robots moving around the arena and can all be avoided if you're up here. Should you get hit by one, keep trying to do evade moves to get out of their way.
Some tougher enemies with melee attacks. Just snipe them.
Some gun men that are easy to snipe.
More mutants. Use a lot of bullets.
Mini boss - bounty hunter soldier gun man (same one from third encounter) and a few normal gun man.

*Note that this encountered fairly bugged. Enemies consistently get trapped in spawn (including the mini boss) and sometimes a sumo mutant who cannot be killed by bullets appears. For the invincible sumo you have to get him run over by a spinning machine.

Shotgun or automatic shotgun. Again, I would choose the automatic.
This time you must destroy the two power generators (one at each end of the arena.) Until they are destroyed, endless enemies will spawn. This is a good place to get your score up if you want a better spot on the leader board.
Each generator takes about a whole round of shots. Once one is destroyed, the shocking defense they put out for you is gone. You'll want to stay away from the center to avoid the shock damage.
As soon as one is destroyed, enemies will come at you. So I recommend shooting each one down about halfway first (8 shots with auto shotgun). Then destroy each one (2-3 more shots).
***Note that the HUD will display "Wave 1/5" at the top. This is a bug as there is only one wave in this encounter.
One of two generators that must be destroyed.

You get the raging bull. This gun does 100 damage per hit and is the most power weapon in the game.
The final boss is a giant teddy bear who unleashes armies of mini teddy bears. Their damage is an instant kill and they can trap you. The best approach is to take out the boss right from the beginning of the level. It's dark and hard to see. He enters the arena from the same gate you do so just turn around. Shoot his head multiple times. When the mini bears start to form a trap around you, shoot one of the trap panels a few times until it is destroyed and then quickly run through it to get away! Eventually the boss will walk next to a barrel, blowing it up will kill him.
Good luck!

This is a failed attempt - took too long taking a screen shot. There is a trap forming around me.

I just wanted to briefly outline the second DLC arena. This one is easier than the Dirty Arena and doesn't require a full guide. Assuming you already completed the main story and Dirty Arena, here are some pointers:

• This DLC consists of 6 encounters with no boss fights. Each encounter starts with a weapon pickup and the final, fifth wave ends with a mini boss fight.
  
• Each encounter adds a new environmental weapon, which should be utilized to defeat the majority of the enemies and conserve ammo.
  
• Although you are also given a Pacyfikator, I wouldn't recommend ever using it. It's more of an annoyance than anything as it will auto switch to this when out of bullets and you just have to switch back. There are plenty of ammo stations throughout the map.
  
• Barrels are no longer a one hit kill for mini bosses, although you should attempt to use them and other environment weapons as much as possible.
  
• There is not an ammo depot before entering the arena in this one, which makes the first encounter challenging since there isn't enough credits until the second wave to purchase ammo. Always start each encounter by finding the closest ammo station.
  
• Sadly, there is not a leader board so points aren't much of a concern. Credits still help for the ammo stations.

10/30/14: Added a video guide for the Second Strike arena:

Weapon: Pistol
Environmental: Barrels. Note that half the arena is gated off.
Mini Boss: Cattle prod man

Weapon: Shotgun or Semi-automatic. I'd choose shotgun.
Environmental: Barrels from a conveyor and a cargo crate (shoot open).
Mini Boss: Sumo Mutant. Try to save as many barrels as possible to use on him and his guards.

Weapon: Semi-automatic.
Environmental: 4 generators. When they are sparking (active), they can be shot to do shocking damage to surrounding enemies. Just don't step in the area or it will hurt you as well. Note that the cattle prod men are immune to shock damage.
This opens the other half of the arena.
Mini Boss: The bounty hunter - he's too hard to kill with shock damage. Just evade roll up to him and shoot him point blank for a couple of clips and he goes down easy.

Weapon: Machine gun or auto-shotgun. I'd choose the machine gun since snipers can be difficult here. There's one up in a crane around wave 2 - take him out (there's a barrel up there) and it makes things much easier.
Environmental: Flaming pipes. Shoot the hole in the bottom to start up, but just make sure it's not pointing at you.
Mini Boss: Bunch of fiery explosion men. The electrified generators work well (save them until wave 5 while they're all active.)

Weapon: Raging Bull.
Environmental: 2 Spinning Death machines. I found that the one in the generator area worked pretty well. Just wait behind it in its stopping position and follow it to the other end. Repeat.
Mini Boss: Cattle Prod or bounty hunter hybrid. He dies pretty fast.

Weapon: Machine gun or Auto shotgun. Shotgun works well, especially on the mini boss.
Environmental: 2 Shocking circles of light. Try to get a majority of the enemies inside the circle when the shock damage comes. Make a lap or two to the other side until it kicks on again and repeat. The middle area between them is also a good place to stop before the circles activate as it has good cover.
*A little secret here is that one of spawn areas where a circle forms has a no clip door so you can walk through the door into the spawn area for good cover.
Mini Boss: large flame soldier.