So there are a few things that should be mentioned that the original explanation doesn’t go over.
1. You will have to complete all 140 side missions to get this achievement.
2. More importantly than number 1, you must complete “Where’s the Wookie” global challenge in order to get this achievement.
It should also be mentioned that you only need to collect the original characters. Additional characters bought through expansion packs do not add to your total or help with this achievement.
“Where’s the Wookie” is likely to be the biggest challenge for folks, but If you’re reading this before heading out on the game, make sure you find the Wookie on each level as you’re grinding out the bricks/challenges. This will avoid having to go back and do it last when you discover it’s the last character you need for the achievement.