Hawkeye beats the Grandmaster. Avengers Annual 1987.
The cosmic being Grandmaster just decimated the Avengers--both East and West Coast teams--using his revived henchmen, the Legion of the Unliving. They overpowered and killed the heroes, except for Captain America and Hawkeye. But Hawkeye tempts the Grandmaster with a guessing game, and cheats him. This distracts the villain long enough for the embodiment of Death--his prisoner--to break free, and send her captor away. She revives the Avengers soon after.
Yep, that's Hawkeye. He may not be the master tactician Cap is, and doesn't adhere to the same strict moral code, but he gets the job done, even if it seems like he's just making things up as he goes along.
Also, thank goodness very few villains are omniscient.