616 Bullseye accepts a contract to kill all the Princes and Princes of Amber (era: post Zelazny short stories, so immediately after Hall of Mirrors).
Bullseye is given a magic tattoo that enables him to travel in shadow as a novice Pattern initiate but has no Amber-capable gunpowder, so largely must rely upon weaponry and hand-to-hand. He has basic knowledge of the Amberites.
Amberities have no basic knowledge of Bullseye starting out, unless, possibly/maybe, if they have visions/precognition and so forth (ie. Vaille, Tir-na-Nogth experiences, etc).
NOTE: This is "standard issue" peak Bullseye, as he is/was at his archetypal, goes toe-to-toe with Daredevil, level of performance, regardless of his current state in continuity. So if he's currently crippled or hulked out, ignore that.
Apparently, Bullseye has some admantium in his skeleton (?), so if that meets the requirements of standard equipment, include this. Not sure why it wouldn't slow him down or kill him, but just assume "magnets" and run with it.
How does this play out?