To unlock the Green Loontern AKA Daffy Duck, you need to do the following:
A: Beat every story stage that takes place in a Lantern Planet
B: Complete his mission in the Watchtower that gives you access to the Moon
C: After collecting a certain number of Gold Bricks, unlock the Lantern Planets on the Moon by building the portals (Oa is not necessary for unlocking Daffy)
D: Complete every Green Loontern mission in the Lantern Planets, some are a tour around the planet, others involve you finding something (or someone for him) and some miscalleneous ones
Once you unlock him, complete any hub race as him and you'll get the achievement
Advice for any "Find someone" missions:
They are always close to where you started the mission, the areas usually have multiple paths so go to each path and you'll find it after a few seconds
Ambush Bug's mission for example needs you to find 5 bugs, and the area he is at has 5 alternate paths and the bugs are not far away at all, following these paths and going back to the starting area after finding each bug makes it hella easy
If you still don't understand, ask me to make a video explaining it.