You have to buy items from voidmudkip (up your room).
Each pokemon has one item that give more points.
You can feed to give more stamina (the feed is also bought from voidmudkip).
And i had a hard time finding it, but to progess the day (so you can feed them more), you have to sleep on your bed.
I have heard that hybrids are quite strong (like pseudolegendarys, but you can beat up to the current version without them).
PD: Get the free popplio from voidmudkip, the last hard bosses (from this version) are fire and dark type.