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.
Unlock a golden chest with the Explorer's Key.
Die 50 times.
Collect 15 Monster Logs.
Find the bloated survivor.
Deal 5000 damage in one shot.
Bank 20,000 gold.
Find the robot janitor.
Collect 4 Keycards.
Kill a boss with 'Lights Out'.
Survive 40 minutes.
Pass a shrine 4 times in a row.
Fail a shrine 3 times in a row.
Kill the Magma Worm, Wandering Vagrant, and Giant Stone Golem.
Defeat 20 lemurians in one playthrough.
Drown 20 Whorls.