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