Here is the full list of all 24 Ratergy achievements.
Win a normal match with the white rats.
Win a normal match without getting any cheese chunk from the big cheese.
Win a normal match with the brown rats.
Bring your first cheese chunk to your nest.
Hit your first enemy rat with an attack.
Bring 50 cheese chunks into your nest.
Bring 500 cheese chunks into your nest.
Hit two enemy rats with a single attack.
Hit three enemy rats with a single attack.
Hit four enemy rats with a single attack.
Win a normal match with the black rats.
Win a normal match with the grey rats.
Play 10 matches reaching the score screen.
Play 100 matches reaching the score screen.
Bring a cheese chunk to your nest while speed powerup is active.
Hit a nest that has some cheese in it with a bomb.
At least three rats are hit by a bomb simultanously.
At least six rats are hit by a bomb simultanously.
Apply at least two speed power ups on the same rat.
Hit an enemy rat while shrunk.
Shrink the same rat at least two times.
Hit at least two enemy rats with the cat paw.
Win a match by playing with both your rats an almost equal amount of time.
Destroy at least 20 cheese chunks during one match (Bombs, Cat Paw)