I DO NOT claim to be highly ranked, however I can give a few tips to help improve your combat effectiveness as Assault.
Be the one to draw out the monster. Communicate with your team, and let them know to stay a safe distance back whilst you run into where the monster has setup shop to lure them out to your team. Everybody running into a cave with a Behemoth is exactly what the Behemoth wants you to do. By sending in only one person, and the most durable individual, this has not gone to their plan, and they must either fight where your team wants to fight, or wait out the dome, and try again somewhere else.
Be a bit stingy with your Personal Shield. Whilst in certain situations it can be ideal to activate your shield, try to use your shield when you are at healf health or below. Activating your shield directly once you engage does not do much but tell the monster in a few seconds you won’t have any protection (besides Supports). Try not to use it the instant your get pounced. Also, do not use it if you are at full health about to take a Rock Throw, Fissure, etc. directly to the head, as your medic can heal you to full if you use it when the monster decides to try to finish you.
Use the Personal Shield for defensive purposes, unless it calls for offense (monster has only 1 health bar left, etc.). When you use your shield, do not continue to push the fight. Back off and allow your medic to heal you, unless it calls for offensive use.
With no Medic, or health regen, whilst at low health, fight carefully. If you are below half health with no medic or health regen, consider fighting hit and run, especially as Lennox. Back off and wait for the monster to turn their back to you. When they do, go and burn, shock, shoot, and lance their back off until they start attacking you. When they start, pop your shield if you get too low and run.
Hope these tips help!