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.
Drown 20 Whorls.
Find the robot janitor.
Find the bloated survivor.
Kill a boss with 'Lights Out'.
Unlock a golden chest with the Explorer's Key.
Collect 15 Monster Logs.
Deal 5000 damage in one shot.
Bank 20,000 gold.
Survive 40 minutes.
Kill the Magma Worm, Wandering Vagrant, and Giant Stone Golem.
Pass a shrine 4 times in a row.
Defeat 20 lemurians in one playthrough.
Fail a shrine 3 times in a row.