Really good question. Peter cannot trigger during Battle Resolution, as nothing can be played nor activated during that time, and he also cannot trigger while another effect is resolving. Therefore:
1. Your EC is discarded.
2. Fool is rescued.
3. Immediately, Fool is triggered as a result of being rescued. Peter still cannot be activated.
4. Heroes in battle are discarded.
5. Great Image activates, as the battle has ended. This is an ongoing trigger that activates at this stage, and Peter still cannot be activated (cannot insert during Great Image).
6. Peter is discarded.
Now Peter is out of play, he cannot be triggered for the heal.
