Here is the full list of all 26 Chompy Chomp Chomp Party achievements.
Dash between 5 zones without getting chomped
Dash between 3 zones without getting chomped
Win a round of Chase & Chomp without being chomped
Play a round of Chase & Chomp without chomping anybody
Reach a x5 multiplier in a round of Chase & Chomp
Chomp 1,000 chompies
Chomp 10,000 chompies
Chomp 100,000 chompies
Eat 1,000 power ups
Eat 10,000 power ups
Eat 100,000 power ups
Dash between 10 zones without getting chomped
Win a round of Ghost without being chomped
Win a round of Cake & Chomp by winning every cake wave
Win a round of Cake & Chomp without ever winning a cake wave
Complete a cake wave while also chomping 5 chompies within that wave
Chomp all other Chompies before the next sandwich spawns with 4 players or more
Get the Thing first and keep the Thing for an entire round
Win a round of Chase & Chomp without using a power up
Eat 1,000 cakes
Eat 10,000 cakes
Eat 100,000 cakes
Eat 1,000 fruits
Eat 10,000 fruits
Eat 100,000 fruits
Play a round with each colour chompy in any game mode