Avoid making any penalty/care miss, although it depends on the digimon that you want. Some require you to intentionally make those mistakes.

Try to clean up poop/lights off/feed within 20 minutes.

Some evolution stage require minimum number of battles to evolve, like 30,70,100, and certain win percentage. If those are not met, it wont evolve.

It seems like hard but really, its a fun game