In this context, Hawkeye likely refers to Clint Barton, Jeremy Renner's character from the MCU, and the owner of the Hawkeye name before Kate Bishop.
Yeah... once I looked him up, that does make far more sense... I am so not up to date on comics or cinema universes.
I do not think I've seen all that many non-cartoon based superhero movies in the last couple decades... the X-men ones with Patric Stewart, the first Iron Man, the first Spider Man, and the first two Fantasic Four (my mom is a fan), and the Thor movies(if they count) and part of Aqua Man (mom again). I have been tempted to see the Wonder Woman movie from a few years ago, but have not done so yet. I've seen a few bits and pieces of a half dozen or so others (like later spider man movies, WTH happened to MJ, ick). I know of two differing Shield attempts, one with a black guy and one with David Hasselhoff.
Nothing I've watched though has managed to keep my interest though. Terrible plots, resets, and bad acting galore. I just don't get how Iron Man for example could possibly have been popular.
Last cartoon/anime of superheroes of this type I think would probably be Wolverine and the X-Men (I really liked it, but no other seasons)... oh and the first episode each of X-Men and Wolverine manga style cartoons from ten years ago... Blegh...
EDIT: I take that back... there was one I have seen, if you count it, as a animated superhero series.... The first season and 3/4ths of the second season of Where in the World is Carmen Sandiago... quite the innovative remastering of the tried and true concept...