Character upgrades are similar to Combat upgrades and are actually listed above them in the upgrade menu. They are golden and require golden spiders to unlock. To gain golden spiders you must collect the throughout the chapters (specific amount per chapter). Also, when getting a gold medal on a challenge, you will obtain one. You will not likely have enough spiders by the end of the game to be fully upgraded. Even after collecting all spiders in the chapters, you will have to get gold medals in challenges to finish them off.