The key to DMR fights is movement and accuracy. Strafing is the easiest movement method, and a good strafe can mess virtually any shot up for your opponents. There is
NO set strafe that will work better. You want to develop a personal strafe that goes in all directions. When you master this, try adding crouching, jumping, and crouch-jumping as well to throw off even more shots. The tricky part is hitting other players while your bouncing around and often they're strafing as well. This takes time and practice, but don't worry it will come. If you have a friend around your skill level, work together in training. 1v1's and map exploring also improves your skills and it will give you another set of eyes to spot any weaknesses in your game.
Any questions, feel free to ask

P.S.
During reload, if you switch your weapon twice quickly as your character slides the magazine back into the DMR, you will recover slightly faster. This could give you the half second you need to get that last shot off. Please note that this also takes practice. If your timing is off you will cancel your reload and be out of ammo mid-fight.