In my arsenal of adhesions, I use a lot of E-6000 (keeps rank bar caps on even after dropping them god knows how many times, I have done several runs for other people in my area and none of them have said any of their caps have fallen off to this day), Shoe goo (which I admit sounds really odd, but its from the same makers of the E-6000 but sticks to a lot of surfaces and has a much harder dried surface than the E-6000), Super glue (sometimes you just need a spot wield that is quick to hold) and gorilla glue (but I only use this if the project has two surfaces that are resisting each other in some way)
But on the hasbro helmets I have a lot better luck using the E-6000 and Shoe Goo more than anything else. And I think I used about everyone of the others to try to glue in some new cheeks on my J2P helmet and nothing stuck to the plastic.