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Well, the title is self-explanatory.

Superman gets to punch Gipsy repeatedly until the jaeger is no longer operational. For people who have not seen Pacific Rim 2, 0:35 here gives you an idea of the kind of hits Gipsy can take:

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So, how many hits?

Derp, I misspelled Gipsy in the title.

Also, just to clarify, Superman can use his flight to hover off the ground, so that he isn't just punching at Gipsy's feet, but he can't use his flight to add extra momentum behind his strikes.

Kinda depends where. I'm sure a solid blow to the head would bring her down.

I think a headshot could knock it over, but not sure if it would be damaging enough to actually render Gipsy out of action. It was still running after sustaining head damage during the film. The impact might kill the pilots though.