To make it simpler, think helmet is a sphere.
Now I need to place a star or any other complex object you can think of - on it. It's a big star, and it looks like taking the half of the helmet - so it should be spherically bent too. It can be separate object.
(P.S. I watched another tutorial where the guy used boolean modifier in order to intersect two objects. The booleans seem to work on simple object. It didn't work in my case.)
I would suggest you use a shinkwrap modifier, as well as a solidify modifier to give it some thickness, and possibly a bevel:
This applies to any shape you'd like to project onto any surface.
Just keep in mind that you need to have enough geometry to allow it to deform smoothly, and preferably a quad loop around the border to avoid shading (or bevel) artefacts:
Starting with a sphere and a star as separate objects, align the view so that the view is straight on to the star (in the second image I used front view).
Select the star then the sphere, enter edit mode. Look oven on the tool shelf and press the Knife Project button. This is what you will get.
