Either locate the costume icon in-game on the indicated level or beat the specified difficulty setting to unlock the corresponding costume. When they have been unlocked the costumes can be selected at the 'Profile' screen.
Coipel Thor (Oliver Coipel Designed Costume)
Vanaheim (The Arrival); after charging the first door and going through it stay on the overhang and walk behind the tower with the door.
Destroyer Thor (Destroyer Wearing Thor's Cape and Holding Mjolnir)
Beat the game at any difficulty.
Kirby Thor (Jack Kirby Designed Costume)
Niflheim (The Approach); after throwing the statue head, it's to the right of one of the giant stairs.
Ultimate Thor (Ultimate Avengers Costume)
Midgard (Burning Town); in the same area where you saved the trapped civilians from fire outside the police station.
Frostgrinder Assault Mode
Complete History Mode.
Odin, Heimdall, Loki and Sif in Frostgrinder Assault Mode
Clear Frostgrinder Assault Mode with any of Three Warriors: Hogun, Fandral or Volstagg.
Ragnarok! difficulty
Complete the game once on any difficulty setting to unlock this bonus feature.