Here is the full list of all 27 Chompy Chomp Chomp achievements. It takes around 1-2 hours to unlock all of the achievements on Windows.
Use the teleport power up 5 times or more in one round of battle mode
Use the gas cloud power up 5 times or more in one round of battle mode
Get 20 chomps in a row without being chomped in battle mode
Get 10 chomps in a row without being chomped in battle mode
Reach a x5 multiplier in a round in battle mode
Pick up 5 or more poisons in a round
Play a round without being chomped in battle mode
Play a round without chomping anybody in battle mode
Use every type of power up in a round
Use the invincibility power up 5 times or more in one round of battle mode
Use the bubble power up 5 times or more in one round of battle mode
Use the slippy power up 5 times or more in one round of battle mode
Use the speed boost power up 5 times or more in one round of battle mode
Use the sticky power up 5 times or more in one round of battle mode
Build up a x10 alternating blobbidee chain in arcade mode
Eat all of the purple blobbidees in a bonus round in arcade mode
Clear 8 waves in arcade mode
Eat all of the yellow blobidees in a bonus round in arcade mode
Eat 3 purple blobbidees in a row
Eat 3 yellow blobbidees in a row
Eat 2 yellow blobbidees then 2 purple blobbidees
Eat 2 purple blobbidees then 2 yellow blobbidees
Get 5 chomps in a row without being chomped in battle mode
Build up a x20 alternating blobbidee chain in arcade mode
Clear 16 waves in arcade mode
Clear 32 waves in arcade mode
Clear 16 waves with a friend in arcade co-op