It's a Compound Short Bow. You can kill the dragon for extra souls if you want. But it may be easier if you kill it after getting the Compound Long Bow from 4-2.
I made that tower knight my bitch tonight. And then I was cruising in 3-1, made it down to the first floor in the prison, killed a weird, giant, magic-shooting dust bunny and then promptly walked off an edge trying to chase a crystal gecko. It so stressful in the moment, but all grins in retrospect. I think that's the magic with these games.