Like the achievement says complete all Bounty Hunter missions. Before you're able to start the missions you need to buy all the Bounty Hunters, Boba Fett, IG-88, 4-LOM, Greedo, Dengar & Bossk.
1. R2D2 - Go up both grapple hooks and construct the two gears to extend the bridge. Go through the next corridor and then turn right to find the Bounty Hunter door (with green circle), go through and follow it to left to the two doors at the end (Theres another left but just ignore it). Enter both and LEGO pieces will fly out, construct the door and R2D2 is behind it. Walk up to him to complete mission.
2. Obi-Wan Kenobi - Follow the first section around as if you were playing normally, Get the droid IG-88 to hack the R2 elevator. Step across both sets of buttons to make the switches rise, then use them. (Be ready for the four Storm Troopers, I find Greedo or Fett to be the easiest as they can dodge the bullets. Carry on to the next part and have IG-88 hack the C-3P0 door, through it and Obi-Wan is to the right behind the LEGO bits you can blow up.
3. Chewbacca - Use the grappling hook to get to the next area. As you go through use the grappling point to get to higher ground, then use the second to cross the gap. Flip the switch to release the moveable block, push it along and drop it off the edge. Go down to the level below and push the block right to the end. Once in place shoot it to blow up the door. Run into the big open space and to the big brown doors. Chewie is behind the 1st door on the left.
4. Princess Leia - Build the lever and turn it so you can safely cross the gap. Use both Grapple points, jump the gaps then go through the big door. Be prepared for a few Storm Troopers as soon as you enter. Go through and carry on down the corridor and use the second elevator to go down. Build both switches then use them to open the door, go down and Princess Leia is in the one opposite to the one she was in in Story Mode. (Or 3rd set of switches on the left).
5. Admiral Ackbar - Have IG-88 hack the C-3P0 door to the very left as you start. Use a thermal detonator to blow up the shiny objects to clear a gap through to the next room, (at this point you can actually see him in the machine through the glass). Go through and build the machine next to the glass contraption, once made the glass will open, jump onto it to claim your prize.
6. Yoda - Head left, build the 2 gears to raise the draw bridge, your friends will keep the Ewoks at bay for a bit. Go across the bridge and head towards C-3P0's throne. You should be able to see Yoda in the tree tops at the back, build the lever and rotate it so it levels out the platform, grab Boba Fett and hover across, the platform rises, go grab Yoda.
7. C-3P0 - Go straight forward down the corridor, up the stairs, continue forward and go through the Bounty Hunter door. Have IG-88 hack the C-3P0 door follow to the left along the corridor to the two elevators, take the 1st on the left up (Bounty Hunter) to the roof top area. You can't miss C-3P0 to the left of where you came up.
8. Lando Calrissian - Across thew bridge kill all the storm troopers and build the grapple pad. Use it to cross and head right, use the second grapple pad and head right again. (Stepping on the button, cutting off the laser makes it a little bit faster for your friends to cross the treadmill). Follow the path to the right and blow up the blue box so the orange one can be moved. Hack the door with IG-88 head all the way up and round, cutting off the gas by hacking the R2 door. Head up then go to the left into the last area where Mr Calrissian is hiding.
9. Luke Skywalker - Go left and up and use a Thermal Detonator on the shiny object. Build the lever and rotate it to straighten up the space ship. Build the grapple pad and use it to climb the ship, you'll complete the mission as soon as you land on the platform.
10. Han Solo - Build the bomb to blow up the door, follow the corridor round and build the heater. Shoot it to melt the ice blocking the door. Go through it and push the heater into place to melt the ice blocking the next door. When you get to the junction turn right and head into the room where you built the train, build it and get on, Han Solo is in the chamber on the right. Grab him and your achievement.
Doing this also unlocks 10 Gold Bricks to help towards the 100% achievement.