Here is the full list of all 12 Contra achievements worth 200 gamerscore. It takes around 5-6 hours to unlock all of the achievements on Xbox 360.
Complete the second tunnel with a score of 100,000 or more in Arcade mode.
Collect 3 different weapons in the second tunnel.
Beat the first timed tunnel with 33 seconds or more left.
Beat the second timed tunnel with 55 seconds or more left.
Get to the second tunnel without obtaining a single weapon upgrade.
Get to the first tunnel without losing a life.
Collect 4 different weapon power-ups.
Destroy the alien tower at the end of the water level.
Score 100,000 points in an Xbox Live Co-op game.
Complete the game in Xbox Live Co-op mode.
Complete the game in Arcade mode using only 1 credit.
Complete the game in under 12 minutes.