Here's a breakdown of what you have to do to win all the awards in the game.
Artisan: For understanding art, like really understanding it -- Paint and fire 12 vases. This is time-consuming, no question, since each vase takes 5 minutes real-world time to fire. One way to do this is to put a vase in the kiln, then leave the game running and go do something else, like housework or homework.
Cagey: Because no cage can hold you! -- Trip the cage at least seven times. After you get the activation code from Xenia's box, go down to the cage in Tartarus and enter it over and over. You can do this before you get trapped or after Thanos escapes, either one.
Previewer: For being very patient -- Listen to all of the audio tracks in the Player app on the office computer. No wonder they talk about patience. This stuff is pretty funny, but there is an awful lot of it. When you first gain access to the computer, there are only a few tracks available; the rest show up throughout the game, so keep checking until you see 10 groups listed on the left. I believe you can just click on the fast forward button, but they're worth listening to if you have half an hour to kill.
Restorer: Restoring culture, one pixel at a time. -- Solve all seven images on Xenia's tablet.
Spoiler Free: The Best in Skull award for pretty ideal brains -- Finish the game without using any spoilers. You can go into Nancy's phone and use a hint, but if you read all the hints for a problem you've been spoiled.
Ticket Agent: For charging exorbitant fees for literally no reason at all. How do you sleep? -- Solve all available levels in the Ticketer app on the office computer. Some of them are easy, some are ridiculously hard.
Trivia Tamer: For systematically trapping and domesticating wild facts -- Correctly answer the trivia question at the end of the game.
Wannabe Hero: For knockin' on heaven's door -- Try opening the gold Elysium door 30 times. This is the door to the right of the judgment scale in the Underworld. The door will never open no matter how many times you click; did you think it was easy to get into heaven?
Charmed (Bonus Edition only): For finding all but one charm ;) -- Find all seven phone charms. I know it says "all but one," but as far as I can tell, there really are only seven charms.