Here is the full list of all 16 Contra Anniversary Collection achievements.
Clear Route A in Contra: Hard Corps
Clear Route C in Contra: Hard Corps
Clear Route B in Contra: Hard Corps
Clear Route E in Contra: Hard Corps
Clear Route D in Contra: Hard Corps
Complete Super Probotector: Alien Rebels
Complete all games
Complete Contra (Arcade)
Complete Operation C
Complete Contra (JP)
Play each game
Complete Super Contra
Complete Probotector
Complete Super C
Complete Contra III: The Alien Wars
Complete Contra (NA)