The DLC added some hero mechs that can only be obtained by beating mission chains. Here is some basic info about them such as who gives the quests and the negotiation bonuses, what is the required reputation, drop weight requirements, and enemies faced. Also included are some tips for beating the missions.

Reputation 6
Play as Kurita vs Crimson Inclination (Outlaws)
Reward Dragon SDW (damaged)

Mission 1 Beachhead 230t
This mission has several artillery and several hidden artillery units. Hidden ones can be destroyed without ever attacking if you kill them before clearing the base.

Mission 2 Demolition 270t
Mission 2 is a straightforward demolition mission.

Mission 3 Assassination 315t
This mission consists of a custom dragon and several heavy mechs and vehicles. Super small map where you'll get swarmed.

Mission 4 Custom 50t
Mission 4 is a weird map where you must kill com towers within 20 seconds. Lots of small vehicles attack you along the path. At the end is 5 mechs from 20t to 60t that you're supposed to lure into an ambush with a fast mech but can kill fairly easily with a good hunchback. Mission wants you to bring jumpjets for a couple of swamp patches that slow you down. Jumpjets are completely unnecessary.

Reputation 7
Independents vs Davion
Last mission is independents vs independents and you'll lose double massive rep with them
Reward Rifleman DNA (damaged)

Mission 1 Defend 290t
A friendly rifleman and 2 vindicators help defend. Enemies include a centurion, shadow hawk, 2 vulcan, rifleman, a cicada, nobody cares locusts, firestarters, dervish jagermech, urbanmech, javelin, and spider.

Mission 2 Raid 295t
There are 4 areas: rifleman, hunchback, javelin in one, jenner, vulcan, centurion in two, urbanmech, shadow hawk, banshee in three, and 2 vulcans, a javelin, and a phoenix hawk in four. A dropship dumps a quickdraw and locust.

Mission 3 Demolition 310t
This mission has a locust, javelin, cyclops, shadow hawk and is reinforced with a blackjack and shadow hawk. A dropship dumps a centurion and hunchback.

Mission 4 Assassination 270t
This mission has a ravine with LRM and long range spamming enemies across it out of range of short range weapons. First group is an archer, jagermech, trebuchet, and blackjack. Second is a warhammer and a blackjack pair. Defend final area from enemies shooting down from ridges. One side has 2 ravens and 2 cataphracts. The other has a rifleman, warhammer, and vindicator. Long range weapons and possibly AMS systems are recommended.

Reputation 8
Marik vs Independents
Reward Archer AGC (undamaged)

Mission 1 Demolition 270t
Straightforward demolition.

Mission 2 Raid 315t
Straightforward raid.

Mission 3 Defend 340t
There is an awesome, charger, and 2 medium mechs. Lots of light mechs run through the base.

Mission 4 Custom 270t
There are 2 paths. South is an optional base. Killing it keeps them from swarming you. Charger, Orion, Thunderbolt, Cicada, and 2 light mechs defend it. North is a settlement that needs to be captured. Only a handful of tanks attack if the south base is destroyed first. Final area has 2 shadow hawks, a jagermech, and a locust. Afterwards, a dropship drops a flea, marauder, warhammer, and orion.

Reputation 9
Play as Liao vs Bandits
Reward Orion YAJ (damaged)

Mission 1 Defend 270t
This is a straightforward defend mission with no lostech mechs.

Mission 2 Demolition 315t
Exotic mechs in this mission consist of a black knight 6, champion 1N2, a phoenix hawk 2, and a flea 17.

Mission 3 Assassination 315t
Exotic mechs in this mission consist of kintaro 19, black knight 6, phoenix hawk 2, highlander 732b, and a champion 1Nb.

Mission 4 Assassination 340t
Mission 4 is a volcanic map with 1 small patch that you might have to walk through if no jumpjets. Bring jumpjets if you want to kill the base off to the right side. It gives a bonus of 987,654 c-bills, but is heavily defended with 2 hunchbacks, a warhammer, and possibly a black knight. Long path with some medium mechs and a final battle against a stalker, phoenix hawk, and a cyclops. Exotic mechs consist of a black knight 6, stalker 3fb, and cyclops P.

Reputation 10
Play as Davion vs Kurita
Reward Victor BSK (damaged)

Mission 1 Defend 270t
This is a straightforward defend mission

Mission 2 Beachhead 315t
This mission has an absolutely obscene number of artillery half of which are hidden and open fire when you start to claim the base. Really bad visibility. Ends with an anticlimactic light mech final attack.

Mission 3 Raid 350t
This is a straightforward raid mission.

Mission 4 Assassination 400t
This mission is a low visibility ice map. Can go the side route. Random ecm towers along the sides. Dozen light mechs, 2 medium, and a charger. Ends with a full assault lance including a stalker and a marauder 2. Haven't tried the direct attack.

Reputation 11
Pirate vs Steiner
Last mission is Interstellar Exp (Independents) vs Oberon Conf (Outlaws)
Reward Corsair PVT (damaged)

Mission 1 Raid 340t
This mission has super low visibility. 1 orion, 1 quickdraw, 2 medium mechs, and tons of light vehicles. Be able to swat vehicles fast rather than hard.

Mission 2 Raid 340t
This mission has 6 medium mechs, a stalker at one location, dragon, quickdraw at another, huge swarm of missile vehicles, vtols, and turrets. Again, swat vehicles fast.

Mission 3 Demolition 340t
This mission has a banshee, 1 crab. Rifleman, locust, and phoenix hawk arrive later. Easy money.

Mission 4 Ambush 380t
This map starts off walking into the middle of a pirate base in what seems like an obvious pirate trap. Instead, Oberon attacks in 2 dropship waves and you win after defeating them. First wave is a griffin, dragon, awesome, wolverine, banshee, grasshopper, and urbanmech split between each side of the base. Second wave is a single dropship with a thunderbolt, charger, jagermech, and corsair. The pirates are friendly and pilot a quickdraw, grasshopper, jagermech, and shadow hawk that will help you.

Reputation 12
Steiner vs Militia (Outlaws)
Reward King Crab CAR (damaged)

Mission 1 Demolition 400t
This mission has a locust, phoenix hawk and awesome followed by a charger, blackjack and urbanmech.

Mission 2 Demolition 400t
This mission has a victor, black knight, and locust followed by a blackjack, assassin, and enforcer. A dropship lands an archer and a centurion.

Mission 3 Raid 400t
This mission has a hunchback, awesome, thunderbolt, catapult, javelin, and a stalker. They are fairly spaced out and you shouldn't have to fight more than a couple at a time.

Mission 4 Beachhead 400t
This mission is a mess. Start out on the shore of a very small map with with 8 artillery firing at you, 4 on each side of a hill in front of you. You have 2 friendly assault mechs and a line of vehicles. Immediately start off in battle with a warhammer, griffin, shadow hawk, vulcan, marauder II, and rifleman. Attacking the base on the hill yields a shadow hawk, griffin, charger, and vulcan. Dropships come like crazy dropping off another shadow hawk, griffin, vulcan pack followed by the king crab along with an awesome, archer, and vulcan. The whole time, vtols will continue to send swarms in waves. There were so many mechs swarming, I might have missed a few. Salvage list has tier 5 Ultra AC 5s and tier 5 LRMs for outfitting the CAR.