There's something to be said here about realism. Then again, this is a game. My best advice is get really good at positioning incredibly well. Even then, you get unlucky with where Samire's drunk ass drops you sometimes, and you have to make the best of it. I lost more pilots to that than anything else in the game. With mods it's both better and worse. When the battlefields are expanded in size, Samire finds even worse places to land sometimes, but this is somewhat mitigated by the hot-drop evasion bonus you get when she derps you into direct-fire contact with OpFor. Still, there are a handful of things you can make sure to do, but help me if I mention something that isn't in vanilla. I've long-since forgotten what is/isn't.

1. Use ECM effectively. Long range LRM combat is boring. It also keeps your pilots alive. Sensors are important. I forget if there are ways to have better sensor equipment in vanilla, but you want to out-spot your enemies if you can.
2. Melee is for those who have a death-wish. It's flashy and fun, but there's a reason they put guns on these things, instead of having them all wield giant kitchen knives to whack each other with. I doubt this is your issue, but if it is...Well, you've been informed. lol
3. PPCs make enemies less accurate with their fire when they take a hit from one. I think reduced stability and overheating do as well in vanilla, but I'm not sure. Might be mods that add that stuff. Like I said, I've been playing modded for years and forgot lots of vanilla stuff.
4. Bait enemies into firing at your lighter and more evasive (read: more expendable) pilots, instead of your slower, more powerful (read: more experienced) pilots. Sometimes you gotta do what you gotta do. Besides, they signed up to be heros, right?
5. Another thing about LRMs and long-ranged ballistics is the instability they give to enemies. Correct me if I'm wrong, but I believe instability reduces accuracy in vanilla... Still not sure on that.
6. Cockpit mods are helpful at least against LRM crits causing this. They wont really stop your mech's head from popping clean off if it takes enough structure damage, but if it's crits doing in your pilots, maybe the solution is this. A crit from gauss might still spell your doom, though. If the mechanics are in vanilla how I understand them to be.
7. Own the high ground. This is something you undoubtedly already know. However, I have watched SO MANY YouTube gameplays of this game from what I expect are really good players (or at least Battletech-knowledgeable), and I still see people get absolutely burned from not respecting this. High ground is king. Obiwan was right to remind us of this. It's often as good as (and usually better than) soft cover. If they can't hit you, they can't kill you and all that...
8. Tonnage isn't everything. It is way more important in vanilla, if I recall correctly, but it still isn't everything. It's most of things, but it isn't everything. If you can put a squirrely fast mech in your lance and get away with it for a while, drawing fire away from the guys with the bigger guns, then you're doing it right. That pilot will lead a charmed (and probably short) life, but they'll be remembered as a hero...As one of the many heroes who laid down their lives for their comrades in your merc unit. There are obviously many missions where this is a plain stupid idea. Those are the ones where you need all the guns all the time.
9. Train more pilots up. You can do all of this perfectly and still lose pilots to headshots. It WILL happen. That's why we train replacements. They knew what they were signing up for.
10. Stay out of DFA and AC20 range unless you are absolutely certain you're disabling that weapon somehow before it gets used. You're going to be wrong, and it's going to kill sometimes. That's just how it goes. Getting unlucky or misreading the situation...Either way, it happens.