I’d start by making a template out of paper or card stock. I would literally make a tube that my head can fit in, and then (while wearing it) mark my nose/eyebrows and chin. Then take off the tube and draw the opening, taking into consideration the markings. Cut out the opening and then put it back on for adjustments. Just cut and tape as needed to make it fit comfortably while allowing you to easily put it on and take it off.
Once you’re happy with the mockup, turn it into a pattern by cutting it into pieces. The more pieces you cut it into, the more rounded the helmet will be.
If you want to start with a base instead of making your own, I would look for a magneto helmet papercraft/pepakura file. It’s close enough that you’ll only need to make a couple alterations.
Once you’ve cut your cardboard pieces out, tape or hot glue them together and cover with tinfoil. If you’re working with corrugated cardboard, you can add rounding by rolling your piece of cardboard into a tube with the ribs (lines) going horizontally.
These links may help you see how rounded shapes are made with materials like cardboard:
Craft foam (EVA foam) is better at creating rounded shapes and is generally a more durable material for armour. You may want to use it instead since it will be covered by tinfoil. This tutorial is a good reference for a similarly shaped helmet done in EVA.
You may want to pre-crinkle the tinfoil to get the same look as professor chaos.