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The gameplay for Last Soldier is quite straight forward.
You are a soldier stationed in the jungle, who is facing attacks by giant mutant spiders.

Click fast on the spiders to shoot them.

Shoot those nearest to you.

However, if you are being overrun, and you don't have enough time to kill the spiders closest to you before they take a bite from you, then shoot the closest spiders that you are able to kill - there is no point shooting spiders if you can't finish them off in time, as once they bite you they disappear and are therefore no longer a danger, so it is better to concentrate on the ones that you can kill. That way, you can take a few bites and still survive.

Click on the coins on the ground to collect them, so you can spend them in the shop (campfire). Some coins may roll away, so click on those ones as fast as you can.

When the campfire icon appears in the top right of the screen, click on it to spend coins to upgrade your gun and buy barriers and explosives.

For the later waves of spiders, clicking on the campfire icon is a very useful tactic (even if you aren't going to spend any coins).
Clicking on the campfire icon (which activates the shop) will clear the screen of all spiders - very handy if you are about to be overrun. However, be aware that doing so will also clear any coins which haven't been collected.

Upgrading your gun increases its damage level.

Barriers are very useful for keep back spiders coming from your right and left; there are no barriers to stop spiders attacking from below.
You can only have one barrier on each side at a time (i.e. even when you have enough coins to buy additional barriers, you can't).
When spiders reach the barriers, they start to damage them. Unfortunately, there is no indicator of the current level of barrier strength, nor can you replace existing barriers - you have to wait until they are destroyed before you can replace them (they can only be replaced when the campfire icon appears).
Shoot as many spiders as you can before they reach the barriers (to keep the barriers as undamaged as possible).

You can place up to five land mines and one red explosive cannister (the game determines where they are placed).
The explosives are one-use-only, and explode when they are touched by the spiders. They can only be placed when you buy them from the shop.
I haven't found them to be of much use, so I suggest that you keep your coins for your barricades and gun.

Miscellaneous achievements

Tutorial
[Do the Tutorial in the game.]


Camping
[Click on the Campfire, i.e. activate the shop.]



Coin achievements
I would have thought that it would have made more sense for the pictures for the coin achievements to match the actual achievements - i.e. 2 coins for "Collect 200 coins", 3 coins for "Collect 300 coins", etc. But it is what is is.

Collect 200 coins
As the name says, collect 200 coins


Collect 300 coins
As the name says, collect 300 coins


Collect 400 coins
As the name says, collect 400 coins


Collect 500 coins
As the name says, collect 500 coins



Spider achievements
The spider-killing achievements are now cumulative (the developer made this change in September 2017).

Kill 100 spiders
As the name says, kill 100 spiders


Kill 500 spiders
As the name says, kill 500 spiders


Kill 1000 spiders
As the name says, kill 1000 spiders


Kill 1500 spiders
As the name says, kill 1500 spiders


Kill 2500 spiders
As the name says, kill 2500 spiders


[The notes section has been updated - see the note at the end.]

Notes: At the time of writing (4 September 2017), each of the spider achievements have to be obtained in one game - i.e. to get the "kill 2500 spiders" achievement, you have to kill 2500 spiders without dying.
It can be quite hard to do. In fact, to do so, playing Last Soldier becomes more like a clicker game, as you just spend hours spamming fast clicking all over the screen - there's not a lot of skill involved in doing that, it's more a case of doing it until your hand hurts, and it puts you in the running to get a repetitive strain injury (RSI).

However, on 21 August 2017, the developer said that he will make the spider achievements cummulative - i.e. to get the "kill 2500 spiders" achievement, you have to kill 2500 spiders, although that number can be reached via playing the game a number of times.
If and when that change is made, it will be a vast improvement.
http://sp.zhabite.com/app/681140/discussions/0/1471967615884512557/

*** UPDATE ***
The spider-killing achievements are now cumulative (the developer announced this change on 6 September 2017).
A counter of kills was also added - this counter continues when you restart the game (i.e. it does not reset to zero when you exit the game).
Congratulations to the developer for listening to the players' suggestions.