Which. The tabletop or the PC? I guess my broad tip for both is that your weapons and armor are disposable and your people are also probably disposable and also the mission itself is also usually disposable. The only thing that matters is "can I complete the mission" and "can I get my mechs out". If you can't win, escape and come back.

In the PC game called Battletech my specific tips are to abuse evasive pips (ie: move a lot) and abuse cover (ie: put your mechs in places where they take less damage). The rest of it is positioning and just building a good squad. Don't just stand there and alpha strike a full lance while they alpha strike you back. The game is built around the PC winning if you do that because they always have more mechs than you. So you have to try to position yourself to pick off specific mechs first.

Overall though the goal of battletech in any form is "remove weapons from the battlefield as fast as possible". The less they can shoot at you the more turns you get to shoot at them. So whatever you can do each turn to reduce the amount you're being shot at in all future turns is usually the right move.

Anyway I love battletech both the PC game(s if you include MechWarrior) and the tabletop as well. Hopefully you can give it another shot and go for it!

Also don't play the Rogue tech mod. It's extremely hard to the point that I don't think the people who made it understand what makes battletech fun. It's harder than the tabletop rules which frankly makes zero sense in a video game.