If you can't get past the first boss it's pointless playing on as the game only gets harder anyway to get past the first boss do this
You know the room where you meet him? See the windows opposite the door he comes out of? Jump out the window, you're fairly safe here except from the sniping enemies. You'll see the boss turn around and head for the doorway out of the room, take this opportunity to shoot at his head (human head).
He'll then come around to the ledge you're standing on outside the window, so just jump inside the window as he walks back towards the room you're in again and take shots at his head.
Just repeat this process, jumping through the window whenever he gets close to you. You can ignore the sniping enemies if you want, if you stay far away from them then they won't aggro so leave you alone. Or sometimes Parker will keep them busy, focus on the boss, and make use of the sniper rifle you just picked up, it's the strongest weapon you have at this point.
When he's dazed walk up to him and charge a melee attack, melee attacks and rifle shots do alot of damage so will finish him fast.
Don't worry about ammo, you'll pick up plenty from the arena once you kill him.