While not an infinite exactly, Brawling Zen is tremendously difficult to take down except by specific approaches.
When your shield is broken by damage from a foe, you gain one Power token from Brawling, then Zen deals 1 damage back to them. If you don't spend Power tokens on this hit, you gain a second Power token, meaning you can immediately put up a new shield with Tough It Out, arguably before the next damage action comes in.
Traps, Crush, and Armor/Iron tokens can counter this to some extent, but it's pretty difficult to break otherwise.
With a bit of setup (an ally with Dance, the Found an Opening bonus, or access to Chaos tokens), a Frantic Phantom with access to Patient style can gain access to Waiting Game outside their turn without being restricted by Patient's 'one action per turn' limit, letting them take it an unlimited number of times before cashing it out as one big infinite-power action (useful for, ex. Movement to generate infinite Speed for some sort of token action).
Edit: Missed that shield damage does overflow to HP! Whoops!