what you describe is the circle of death. its when both mechs circle around eachother at top speed.
1. variate your throttle. don't run 100% all the time. especially when you're in a fast mech. when you're slower you can turn tighter, giving you an advantage in aiming.
2. be vary of the torso twist level of your mech. some can turn 360° while others are limited. the bushwacker per example, won't be able to turn and fire back if you're on his back, while a vulture or Raven can.
3. use and be vary of your environment. if you run into other mechs or walls you come to a dead stop, avoid that, but if you have trees or buildings (base) between you and your enemy you can use it as cover.
4. know your mech, know his weapons, the torso twist, the turn rate, the armour levels, and know your enemies mech.
if you have a lasermech don't go directly brawling, stay away a few hundred meters and toast your target while its fighting a brawler variant.
Run away when someone closes in on you and you only got LRMs. RUN.
5. always fight with teammates. lone mechs are dead mechs. the one with the heavier and more armoured mech goes first and draws fire.
6. when faced with heavy weapons like gauss or PPCs or ACs, look where its mounted. when its on the arm, destroy the arm first. preferably with Lasers. A shadowcat without arms is disarmed and can paint a red target cross on itself.
7. know your missile types. LRMs can seriously annoy and damage the entire enemy mechs at a distance. sadly the current maps make it hard to exploit their range. there's way too much cover. ERLRM are heavier and less hard hitting, but fire ludicrous far. ATMs are the most damaging missiles, but have a minimal arming range of 200 meters. they're not brawling weapons. SRM come in 3 flavours. SRMs, dumb fire missiles. SSRMs, lock on missiles, and (C)DualSSRMS, which fire double and faster.
8 line up your shots, keep the lasers on the target, lead for ballistic weapons, /exception LBX, and keep a minimal distance of 100 meter from the target if you can.
9. don't attack Tank turrets. DON'T. the front armor of an atlas has less armour than a Tank turret. attack its sides instead, and keep in cover. NEVER go into a base when a tank is inside. demolishers will eat your face.