All my work is with super glue, so it can be done. BUT, unlike hot glue or elmers once you press the pieces together there is no going back. Just remember to take your time. Another tip is to start at the crown of the helmet and work down. I found it's a lot easier to control when you're always on the edge. Don't rush, it took me a couple of weeks to finish my helmet, and you'll progressively get better and faster when you take your time.
As for glue I've heard everything from hot glue, super glue, Elmer's glue, wood cement, etc. Find something that works well for you and that you like working with.