Unlock characters for 'Free Play' mode complete the following tasks and then purchase them from the store for the corresponding amount of Studs.

Unlock Snowspeeder:
Complete the 'Hoth Battle' level

Unlock K-3PO:
Get ALL cannisters in level 'Hoth Battle' and then buy in the store for 630 studs

Unlock Tusken Raider:
Get ALL cannisters in level 'Tatooine' and then buy in the store for 200 studs

Unlock Stormtrooper:
Get ALL cannisters in level 'Blockade Runner' and then buy in the store for 300 studs

Unlock Probe Droid:
Buy the 'Extra Vehicles' extra and then then buy in the store for 500 studs

Unlock Tie Fighter:
Get ALL cannisters in level 'Trench Run' and then buy in the store for 1000 studs

Unlock Vader TIE Advanced:
Get ALL cannisters in level 'Asteroid Chase' and then buy in the store for 3000 studs

Unlock Imperial Navy Trooper:
Get ALL cannisters in level 'Death Star Escape' and then buy in the store for 3400 studs

Unlock Snowtrooper:
Get ALL cannisters in level 'Hoth Escape' and then buy in the store for 3700 studs

Unlock Lando Calrissian:
Complete the level 'Cloud City Trap' and then buy him for 4400 studs

Unlock Wicket W. Warrick:
Complete the level 'Endor Battle' and then buy in the store for 4900 studs

Unlock Slave 1:
Buy the 'Extra Vehicles' extra and then, you can then buy this in the store for 50000 studs

Unlock Imperial Navy Lieutenant:
Get ALL cannisters in level 'Death Star Rescue' and then buy in the store for 5300 studs

Unlock Gamorrean Guard:
Get ALL cannisters in level 'Jabba's Palace' and then buy in the store for 5800 studs

Unlock Scout Trooper:
Get ALL cannisters in level 'Endor Battle' and then buy in the store for 6000 studs

Unlock TIE Fighter Pilot:
Get ALL cannisters in level 'Death Star 2 Battle' and then buy in the store for 7500 studs

Unlock Darth Vader:
Get ALL cannisters in level 'Cloud City Rescue' and then buy in the store for 35000 studs

Unlock Yoda:
Complete the game and then buy in the store for 75000 studs

Unlock Baby Rancor:
Unlock ALL other characters and then buy in the store for 200000 studs

Unlock Emperor Palpatine:
Get ALL cannisters in level 'Emperor Fight' and then buy in the store for 75000 studs

Unlock MSE-6:
Get ALL cannisters in level 'Cloud City Trap' and then buy in the store for 100000 studs

Unlock Boba Fett:
Get ALL cannisters in level 'Sarlacc Pit' and then buy in the store for 175000 studs