I have some tips, I got these tips way back in Halo 3, and are still useful:
-Dont ever challenge, is hard to do, but, if you see yourself engage in 1 v 1 situation dont let the fight last more than 3 or 4 seconds, if you havent kill this person by that moment, try to change position, and see if another person in your team clean that kill.
-Never see yourself in bottom midle in any map, you are vulnerable from any point in that part of the map, avoid it at any cost.
-When you are going to shoot, always do it from a position where you know you can take cover quickly and have a good route to escape (in this case if you are hit, is ok to drop to bottom mid in a map like Truth)
-work on your straffing and general awareness (like paying attention to your teammates sign and X if they get killed), this will come with experience
-Avoid Sprint as much as you can, there is a small window from when you stop sprinting and can start shooting, not sprinting doesnt put you in disadvantage.
-Try not to pay attention to your Kills and Death, the more you keep checking that, the more pressure you will feel to do better, and you will see yourself rushing.
-Dont chase kills, this is hard one not to do, and more i there is no communication, but you could see yourself like Indiana jones, you have someone you are chasing, and when running to catch him you run into the entire enemy team.
-Shoot any enemy that is in your LOS, even if you are not getting that kill, is better to have that person going to hidding for some seconds than to have him shooting around.
-Try to get party up with people that are willing to communicate, call outs are very important in Halo.