Here is the full list of all 22 METAGAL achievements.
watch intro without skip
defeat GAL02
complete tutorial
collect more than 9 gears
defeat GAL01
defeat GAL03
defeat GAL04
defeat GAL0X
complete fortress 2
complete fortress 3
complete fortress 4
Collect all powerups
Die over 20 times in one level
beat any level in less than 3:40 minutes
Get Rank S on every level
complete all levels in PAR
Complete the game once
Complete the game using gal 01
Defeat Final Boss with Dash GAL
Defeat Final Boss with Buster GAL
Defeat Final Boss with Warp GAL
Finish the game with all characters