Here is the full list of all 15 Risk of Rain achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Die 50 times.
Collect 4 Keycards.
Unlock a golden chest with the Explorer's Key.
Collect 15 Monster Logs.
Bank 20,000 gold.
Find the robot janitor.
Kill a boss with 'Lights Out'.
Survive 40 minutes.
Kill the Magma Worm, Wandering Vagrant, and Giant Stone Golem.
Pass a shrine 4 times in a row.
Fail a shrine 3 times in a row.
Defeat 20 lemurians in one playthrough.
Find the bloated survivor.
Deal 5000 damage in one shot.
Drown 20 Whorls.