Here is the full list of all 20 Teenage Mutant Ninja Turtles Arcade: Wrath of the Mutants achievements.
Complete Shredder’s Lair on any difficulty
Finish the Game on Normal difficulty
Complete Dimension X level on any difficulty
Defeat a Total of 1000 enemies
Complete Amusement Park level on any difficulty
Complete TCRI level on any difficulty
Complete Sewer level on any difficulty
Enter your Score in the leaderboard for the first time
Complete New York level on any difficulty
Finish the Game on Easy difficulty
Finish the Game on Hard difficulty
Eat a total of 100 Pizzas
Use a Total of 100 Turtle Power attacks
Use a Total of 75 Smoke Bombs
Use a Total of 50 Spin Attack powerups
Defeat a Total of 300 enemies using the Shuriken powerup
Use a Total of 30 Team-up powerups
Use a Total of 50 Ice Cream Kitty pack powerups
Complete a Level in 4 player Co-op
Beat the High Score on any level