The Play of the Game system is mostly based on how much of the On Fire bar you accumulate. So in general your best best is to do (or boost) a lot of damage or a lot of healing within 10 seconds, and hope that no one else on the team has something better. The game also prioritizes actions done later in the game (especially overtime). I believe Mercy also gets extra fire if the person she resurrects does good immediately after, but I'm not sure.
However, there are a few other ways to get PotG that occasionally pop up, and are noted by their special subtitle.
- "Sharpshooter" PotGs are when the system decides the distance and movement between you and the people you kill are impressive.
- "Livesaver" PotGs are when you kill an enemy who has just stunned or frozen an ally.
- "Shutdown" PotGs are for killing enemies using ultimates.
For Mercy specifically, one not-all-that-unlikely idea is to kill a McCree, Brigitte, or Mei who's just incapacitated someone, and then heal them as much as you can afterward. Mei is probably the safest to try - keep healing the person being frozen to ensure they can survive the followup icicle, shoot the Mei, and continue healing afterward.