Is that a 6" tall figure?
I usually use some aluminium armature wire to hold my puppets up for jumping and flying. It might take a few strands of 3mm (1/8th") wire to hold it up with my 10" - 12" puppets. Not sure how you would attach the wire, since I don't work with action figures. I generally stick the wire in the back of the puppet, or on the side away from camera. With my foam puppets I sharpen the ends of the wire - 2 strands, so the puppet won't rotate on the wire when i don't want it to - and poke the wire into the foam. The other end is glued into a wood block that I can clamp down to the set, or put in a small vise.
Here's a tutorial I found on Youtube, mainly about painting the wires out, but it does show a Spiderman figure being held up by a strand of armature wire. https://www.youtube.com/watch?v=4mp4tQlylVU I imagine you would have to drill a hole where you want to put the wire.