Maybe some of these may seem silly, but I propose them anyway
- Defeat all players gym
- Collect all pokedoll (if you want you can divide it into collect all pokedolls and collect all shiny pokedoll?)
- Fill "x" pc boxes with shiny (?)
Extreme challenges (?)
- Obtain all shiny legendary pokemon
- Obtain all shiny starter pokemon
- Obtain all special starter pokemon
- Obtain all pokedex shiny (only one of the evolution line is fine)