These are movie versions.
Round 1- Hawkeye is sent to kill Ozymandias. Same situation as the assassination scene in Watchmen. Can Hawkeye kill Ozymandias? Hawkeye has his standard equipment.
Round 2- Random Encounter. Fight takes place in day time in Gotham City. During the day time. Start 10 ft from each other.
Round 3- Hawkeye is in the same situation as Rorschach and Nite Owl at the end of Watchmen. Hawkeye has his standard equipment.
Morals Off. Battles are won by KO or death.