If you're playing as a BA on any Terrain Control map, learn which bases have automated defenses, and stay far far away from them. The laser turrets will snipe you dead in 1-2 hits from 3 zones away.
When you eventually run into a demolisher, make a little "cha-ching" sound and then quickly hop up on top of his turret when he stops. Unlike the partisan, you won't die when he starts moving, and he'll be completely helpless against you. Crouch down up there and start shearing away his side armor with the HML until it pops. Most demo pilots won't have any idea what's going on, or that they're even taking major damage until it's too late, but keep an eye out in case he wises up and decides to bail.
Learn to use your jump jets while still up in the air. Most people instinctively think that their JJs only allow them to travel vertically, but they're actually multi-directional. When you're fighting against someone who knows you're there and is actively trying to kill you, holding down a movement key and using your jets will send you suddenly in that direction. For example, if you hold down A and tap the spacebar, it'll make you jet to the left. Holding D will do the same thing to the right. This allows you to remain unpredictable and helps you to dodge enemy fire.
As others have said, the mPPC has a knockback effect when you fire it. You can use this to your advantage though, with two different ways. One is to fire it in the direction opposite of where you want to move, in order to help you dodge enemy fire, similar to using your jumpjets mentioned above. Another is to help keep you aloft for longer, without as much of a predictable apex at the height of your jump. For example, when fighting an enemy mech at close range, it's often useful to jump directly above him, look down, and fire your mPPC straight down. This will not only make your movements less predictable, but it will also keep you in the air above him for longer, giving you an opportunity to switch to the Heavy Micro Laser for additional damage.
If you're having difficulty fighting other BA, give the mPPC a try. It will kill any enemy Battle Armor with one shot if it's a direct hit, and even if you don't hit them directly it still has considerable splash damage. The trick to using this effectively is to predict your enemies movements, and anticipate where you believe they will land on the ground. Most inexperienced BA will use up their entire jumpjet supply, leaving them very vulnerable for a few seconds after they land. This gives you the perfect opportunity to quickly kill them with your mPPC. When you get more experienced with using this weapon, you can have some fun with trying to pop enemy BA while they're still in mid-air with it.