1. Clear the mission
2. Defeat all pests
3. Defeat all bosses
This is how you get the medals. All three have to be completed in the same run, in order to get the three medals from each map.
Basically, Medals are your completion rating for that map. So, at the end of the event, your final rating for each map (0 - 3 per map) gets added up, and that determines your rewards.