Here is the full list of all 24 Doors Push or Pull achievements.
Purchase 20 Chests
Fail to open a pair of white doors.
Visit 3 Worlds in a single run.
Open 500 Doors total.
Discover the Space Hanger
Crash through a door.
Create a multiplayer room. (You don't actually have to play)
Decorate the Nebula with an Arcade Machine or Slot Machine.
Decorate the Dungeon with Torches, Lanterns, Swords, Staves, Statues or the Dinner Set.
Decorate the Space Station or Hanger with Tubes or the BroBot.
Discover the Dungeon World.
Open 30 double doors by swiping down the middle.
Discover Retro Hill.
Discover the Space Station
Place an item in a room using the decorator.
Decorate the starting hallways with flowers, Christmas Decorations, or the Pumpkin.
Purchase a Velvet Chest.
Open 30 doors in a single run.
Open 20 doors in a single run.
Discover the Nebula world.
Open 10 doors in a single run.
Open a door.
Retry 3 times in a row.
Fail on the first set of doors in a run.