I agree that one brace per rectangle would be fine but I wouldn't do them cormer to corner. It looks like the sort of thing that the kids will inevitably want to climb under so I would just put small braces on each top corner. Maybe just try one short brace on each rectangle and see how you go.
You want them to be big enough to be effective but not that big that they get in the way and the kids will bang their head every time they climb under. Maybe make them 400mm, and as Alex says, make sure they are well bolted on.
Just noticed something else. Close that hook on the top of the rope ladder and get rid of the excess thread on top. That's the sort of thing a kid could get their jumper hooked on and not be able to get off, a real choke hazard if they slip and get hung on it.
So many ideas........so little skill........