Here is the full list of all 15 METAL SLUG achievements. It takes around 6-8 hours to unlock all of the achievements on Windows.
Defeat a boss using the METAL SLUG ATTACK
Play in MULTIPLAYER
Clear the game using no continue
Free 100 POWs
Kill 1,000 enemy soldiers
Free 50 POWs
Clear FINAL MISSION
Throw 200 grenades
Clear MISSION 5
Clear MISSION 4
Kill 200 enemy soldiers
Clear MISSION 3
Throw 50 grenades
Clear MISSION 2
Clear MISSION 1