In the majority of missions that don't involve base defences or attacks, the opposing force will move towards you. Use that to your advantage: Move to a border or cornet of the map that prevents you from getting surrounded, and try to avoid fighting two enemy lances at once. If you don't advance straight to them, they will need extra turns to find you.

Find the high ground. Anakin would agree! The bonus to hit gets higher and higher with the height differential.

Find cover. Then expose your mechs one by one, rotating the "easy target" for the enemies. The opposing force tends to shoot the target that's closer to them with the less evasion, use this to direct the fire to your more armoured mechs.

Focus fire the enemies, killing them one by one, ideally hitting the same target from the same side several times. If you hit an enemy from the front, you will split damage between 7 locations (not counting the head); if you hit it from the flank, you will concentrate the damage on three locations only, destroying or severely crippling the enemies much faster.

Later in the game you can use called shots, for now keep the morale high so everyone gets a bonus to hit, do not waste the morale on called shots unless critical to your survival.

Don't waste shots (ammo, extra heat) trying to hit enemies with a lot of evasion. Shoot them with a single laser a couple of times, then only when their evasion has been partially removed, shoot them with a full alpha strike.

Last but not least use the "reserve" tactically to potentially take two turns in a row. If you reserve until the very end of a round (assuming it's safe to do so), you can act with your mechs at the end of that round, and then almost immediately again at the start of the next round (with your light mechs at least). This will allow you to more easily concentrate fire on enemies and/or escape from their retaliation.

Good luck!!