Here is the full list of all 42 Monolith achievements.
Tarnish notte the majesty! (Acquired all Hats)
Get all 4 S Ranks in one run.
Won the game on Sudden Death Lethality
Get an S Rank in Damage (10 hits or fewer)
Finished a run with a score of 200,000.
Become the reigning tag champion.
Finished a run with a score of 100,000.
Protect Blastcore's smile.
Won without getting any upgrades.
Won without getting any weapons.
Won the game on Intense Lethality.
Get an S Rank in Time (Under 20 minutes).
This is what you wanted, isn't it?
Get an S Rank in Exploration (Visit all rooms)
Pass the seal. (Floor 6)
Get an S Rank in Secrets (Find all secrets)
Leave that poor cat alone.
Defeated the Overlord.
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).
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.