To easily unlock the helmet Carter for your avatar:
Theoretically, you must complete a mission mode Legendary without dying once to access the helmet Carter. If this seems too difficult, there is a method a little simpler. Perform all the same mission on Legendary, but arrived at each checkpoint, save and quit the game. You can then return to your mission at this point and then move in stages without making a single sitting. The risk of failure is much less important.