Here is the full list of all 9 The Search achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Found a secret Ticket Machine
Picked up all Notes & Journal entries
Completed The Search
Journeyed into the Wasteland
Repaired the torn Canvas
Painted the torn Ticket whole
Painted a Crowbar
Painted a passageway forward
Found the first Ticket to another world