Hyperion is a member of the "Squadron Supreme" which were heroes from another dimension. They are basically versions of DC Comics characters - a stand in for the Justice League, which of course Marvel can't use. So, Hyperion is their Superman (Nighthawk was Batman, Sr. Spectrum was Green Lantern....). Due to the nature of the multiverse, tehre may be a few versionos of Hyperion around - it get's a little complicated with those characters. Since they are pastiches of the competition, sometimes they are portrayed in an unflattering light, though that has varied over time.
He has never been one of the Thunderbolts that I know of, but has been on the Avengers proper at times. The sunglasses thing may be new for the game, because I can't recall him ever wearing them - unless it was recent as I don't folow Marvel comics too much anymore.