I mean all Bullseye did was knock some scaffolding on him. Which clearly didn't actually hurt him that much.
And all the help Harry offered was not getting killed long enough for Peter to just punch Bullseye once.
It feels unfair to bring the frustrations of how Lowe and Wells portray a version of Spider-Man that's supposed to have much more experience and be much more settled into his role as a crime fighter to this book.
And yeah this version of Bullseye is trusted by the literal rulers of the world. The secret cabal. The kingmakers. So one would imagine he's likely high on the food chain as far as skilled assassins go