Here is the full list of all 42 Monolith achievements.
Won without getting any upgrades.
Won without getting any weapons.
Reach a highscore of 20 minigames in the Hub.
Finished a run with a score of 300,000.
Finished a run with a score of 200,000.
Reach the Temple.
Tarnish notte the majesty! (Acquired all Hats)
Won the game on Sudden Death Lethality
Get an S Rank in Damage (10 hits or fewer)
Get all 4 S Ranks in one run.
Protect Blastcore's smile.
Get an S Rank in Time (Under 20 minutes).
Won the game on Intense Lethality.
Become the reigning tag champion.
This is what you wanted, isn't it?
Finished a run with a score of 100,000.
Pass the seal. (Floor 6)
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).
Take a screenshot containing 100 bullets.
Admire a fine portrait.