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