Here is the full list of all 25 Combat Cats achievements.
DEFEAT 100 SURFER FISH
SET OFF 2 NUKES IN A ROW
TAP THE TITLE MENU CAT 200 TIMES
MAKE A 4X COMBO
STARE AT THE MAP FOR 2 MINUTES
COLLECT 25000 COINS
COLLECT 5000 COINS IN A SINGLE LEVEL
MATCH TEN BRICKS AT ONCE
PURCHASE YOUR FIRST AIRCRAFT
SET OFF A 6X COMBO
300 KILLS IN SURVIVAL MODE
TRIGGER A LVL2 NUKE WHILE FLYING THE CUPCAKE
COLLECT 100000 COINS
SET OFF 3 NUKES IN A ROW
COLLECT 25 CATNIP
TRIGGER 10 NUKES IN SPACE WHILE FLYING A UFO
DEFEAT 500 SURFER FISH
WIN 10 BOSS FIGHTS
950 KILLS IN SURVIVAL MODE
PURCHASE ALL AIRCRAFT
UPGRADE ALL BLOCKS TO MAX
COLLECT 100 CATNIP
PURCHASE EVERY ITEM AND UPGRADE
BEAT THE CAMPAIGN
UNLOCK ALL ACHIEVEMENTS"