TO beat the back widow easy, first you have to make sure to jump when it fires its cannon. Second, shoot with a S griffon with a long barrel 2 beacause a hand gun does only a little damage. Run counter-clockwise and shoot until it falls on the ground, when it falls on the ground use hand-to-hand combat until it gets back up. Hopefully in about 3-5 minutes you will beat it.

Hope it helps