Invincibility:
Play Episode IV, Chapter 5 in free play mode. Use C-3P0 to unlock the first door, then use someone with force powers to assemble the fridge inside. When assembled, the fridge will open and drop a Super Red Power Block, allowing you to buy invincibility in the cantina for 900,000 studs.

Stud Fountain:
Collect 99 gold bricks.

Lego City:
Get 60 gold bricks and build the doorway outside.

Bounty Hunter missions:
Purchase all the bounty hunter characters (Boba Fett, Bossk, Dengar, Greedo, IG-88, and 4-LOM) to unlock these missions.

Minikit Detector:
In the Cloud City trap level, when you first start, look around the engines of your X-wing and pick up the red power brick.

Achievements

Unlockable
How to Unlock
Bespin - undefeated. (20) Complete Bespin without dying.
Bounty Hunter missions complete. (40) Complete all of the Bounty Hunter Missions.
Carkoon - undefeated. (20) Complete Carkoon without dying.
Cloud City Trap - undefeated. (20) Complete Cloud City Trap without dying.
Dagobah - undefeated. (20) Complete Dagobah without dying.
Death Star Escape - undefeated. (20) Complete Death Star Escape without dying.
Death Star II - undefeated. (20) Complete Death Star II without dying.
Echo Base - undefeated. (20) Complete Echo Base without dying.
Endor - undefeated. (20) Complete Endor without dying.
Episode IV complete. (50) Complete all six levels in this Episode in Story Mode.
Episode V complete. (50) Complete all six levels in this Episode in Story Mode.
Episode VI complete. (50) Complete all six levels in this Episode in Story Mode.
Facon Flight - undefeated. (20) Complete Facon Flight without dying.
Game 100% complete. (180) Complete everything in the game.
Game 20% complete. (20) Complete 20% of the game.
Game 40% complete. (40) Complete 40% of the game.
Game 60% complete. (60) Complete 60% of the game.
Game 80% complete. (80) Complete 80% of the game.
Hoth Battle - undefeated. (20) Complete Hoth Battle without dying.
Jabba's Palace - undefeated. (20) Complete Jabba's Palace without dying.
Jedi Destiny - undefeated. (20) Complete Jedi Destiny without dying.
Jundland Wastes - undefeated. (20) Complete Jundland Wastes without dying.
LEGO City complete. (50) Complete the LEGO City level.
Mos Eisley - undefeated. (20) Complete Mos Eisley without dying.
Rebel Attack - undefeated. (20) Complete Rebel Attack without dying.
Rescue the Princess - undefeated. (20) Complete Rescue the Princess without dying.
Secret Plans - undefeated. (20) Complete Secret Plans without dying.
Secret Plans level complete. (20) Complete the first level of the game.
Speeder Showdown - undefeated. (20) Complete Speeder Showdown without dying.