Here is the full list of all 42 Monolith achievements.
Reach a highscore of 20 minigames in the Hub.
Won without getting any weapons.
Become the reigning tag champion.
Take a screenshot containing 100 bullets.
Finished a run with a score of 100,000.
This is what you wanted, isn't it?
Pass the seal. (Floor 6)
Reach the Temple.
Leave that poor cat alone.
Get an S Rank in Exploration (Visit all rooms)
Get an S Rank in Secrets (Find all secrets)
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).
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.
Won without getting any upgrades.
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.
Admire a fine portrait.
Finished a run with a score of 300,000.