Here is the full list of all 42 Monolith achievements.
Get an S Rank in Exploration (Visit all rooms)
Get an S Rank in Secrets (Find all secrets)
Defeated the Overlord.
Leave that poor cat alone.
Reach the Sanctum (Floor 5).
Reach the Bellows (Floor 4).
Reach the Maintenance System (Floor 3).
Reach the Archives (Floor 2).
Reach the Excavation (Floor 1).
Become the reigning tag champion.
Get an S Rank in Time (Under 20 minutes).
Get an S Rank in Damage (10 hits or fewer)
Get all 4 S Ranks in one run.
Finished a run with a score of 100,000.
This is what you wanted, isn't it?
Won without getting any upgrades.
Won without getting any weapons.
Pass the seal. (Floor 6)
Tarnish notte the majesty! (Acquired all Hats)
Finished a run with a score of 200,000.
Won the game on Intense Lethality.
Won the game on Sudden Death Lethality
Protect Blastcore's smile.
Reach the Temple.
Reach a highscore of 20 minigames in the Hub.
Take a screenshot containing 100 bullets.
Admire a fine portrait.
Finished a run with a score of 300,000.