In order to get all the Achievements as fast as possible you should start with "FIRST GAME!" "VICTORY!" and "LEVEL UP!"

Those require you to win 10 Games in total. But watch out! For every Game you lose you need to win one more!

Win a Game = +10 XP
Lose a Game = -10 XP

To get a Level up you need 100 XP

To win almost any Game I suggest you set up a Game with 4 Bots on the smallest map and then you only click the fields marked in the picture below. (You win when a bot loses, more bots means the chance that one of them dies is higher)


Now you want to get "UPGRADE!"
But to do so you need to be Level 5 and you need to have 1000 Gold. So the grind continues and you need to follow the tactic above until you are Level 5. Then just go to the shop and buy any item.

If you didnt get "LOSER!" yet just lose one Game. The esiest way is to keep pressing the fields arround the statue.

"EXTERMINATOR!!!" is kinda a random Achievement and I am not quite sure on how to unlock it.
You could try to click a field a second time while its falling down. I think that is what it unlocked it for me. (If you know exactly how to get it tell me so I can improve this guide!)