Oh, I was about to calculate how much you could heal their base to be able to attack more than 20 times.
The base solution is “infinite” by moving unlimited +1/+1 runes from a Drill Sergeant (accumulated over however long is needed) onto a Hyperion and attacking once.
Also, my previous solution still works
Summary
: just kill off your own mirror Hyperion with an Archon rune each time it attacks.