For me, completionist in a Pokémon game would be doing absolutely everything it has to offer.
- beating the main story
- catching all legendaries
- picking up all items
- completing all battle facilities (all bosses and rewards)
- trying every side activity at least once and maxing them out if there's progression in it
- completing the dex
- Seeing all secret events and interacting with every NPC at least once.
Not sure if limited time events and external peripherals (Pokéwalker, Dream World etc.) should count.