Here is the full list of all 21 Saiku's Endless Labyrinth achievements.
Complete the tutorial.
Complete the Crystal Caverns.
Find your way out of the cave.
Complete the Winter Wasteland.
Stay for a night in the inn.
Beat Kirsty and get the Spear of the Damned.
Have a mysterious encounter.
Have Dave join your party.
Leave the Mystic Meadows.
You shouldn't have picked that up.
Stray way too far from the main path.
Complete the Forlorn Forest.
Find your way out of the second cave.
Hear the explanation again...
Begin climbing the stairs up to S.A.V.E. Corp. HQ.
Get in the S.A.V.E. Corp. Lift.
Reach the End Credits.
Beat PEROS.
Press the button.
Let Saiku Suffer.
Reboot PEROS.