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.
Clear MISSION 1
Clear MISSION 2
Clear MISSION 3
Clear MISSION 4
Clear MISSION 5
Clear FINAL MISSION
Defeat a boss using the METAL SLUG ATTACK
Play in MULTIPLAYER
Kill 200 enemy soldiers
Kill 1,000 enemy soldiers
Throw 50 grenades
Throw 200 grenades
Free 50 POWs
Free 100 POWs
Clear the game using no continue