Here is the full list of all 10 2 Ninjas 1 Cup achievements.
Kill 15 bees.
Kill 15 wolves.
Kill 15 blue soldiers.
Collect 6 pieces of Sushi. Counted after using a checkpoint.
Collect 12 pieces of Sushi. Counted after using a checkpoint.
Collect 18 pieces of Sushi. Counted after using a checkpoint.
Collect 24 pieces of Sushi. Counted after using a checkpoint.
Destroy the first boss.
Destroy the second boss.
Destroy 15 mechanical soldiers.