Okay, I just want to make sure everyone knows how great my boy All Might is.
My Hero Academia is a world not unlike X-Men, but in it the mutants are the majority rather than the minority. In that world around 80% of the population have some kind of super powers, and some become heroes and some become villains. All Might didn't just became a hero. He became the hero, saving the world countless times and becoming a beacon of hope in the eyes of the general populace, including the protagonist.
To run down his power, All Might can assume his super form which grants him immense physical strength, stamina, and speed. I'm talking hundreds of punches per-second speed. Now, due to a combat injury, he can only channel this power for about an hour, but an hour is enough to do some damage. He isn't invincible, but his powers alone should be enough to get him the win over Archangel.
It all comes down to whether All Might can catch Archangel before Archangel flies away. If Archangel can stall the fight to last an hour and cause All Might's super form to run out, his hand-to-hand combat can almost certainly subdue and defeat All Might. However, there are factors on whether Archangel could even know about this weakness (doubtful) and whether All Might's speed could catch Archangel before his flight takes him too far (likely). Hell, Archangel could go for an attack and get caught, leading to a losing situation.
I don't think this fight is impossible for Archangel to win. However, All Might is an extraordinary individual, and without knowing his main weakness Archangel would lose in a straight hand-to-hand battle.
All Might will win with a well-timed Detroit Smash and knock Archangel out. No Plus Ultra needed.
