What this achievement means by "Completing" is simply beating all the episodes, not 100%ing them, each world has 3 episodes, except for Finding Dory which has 2, Toy Story's episodes are:
1. Daycare Dash
2. Airport Insecurity
3. Dump Escape
Finish all 3 and you'll get the achievement
If it doesn't pop, try replaying the Toy Story levels until this pop, i recommend replaying Daycare Dash as Buzz, as doing that forces the achievements to pop.
Here's a guide for all 3 levels: