Destroying a lair is pretty easy. Either use an infiltrator with the thief perk for 100 stealth and rush the spawnery or use an assault with 20 will points and max speed and a shotgun, dash to the spawnery and 2 hit it or if you have a heavy armor use jump jet but it exposes you and it takes longer plus you can be gooed in place or MCed.
What I find difficult is on the geoscape level. No matter how hard I try to destroy nests, lairs, citadels and keep the ODI as low as possible, they are being spawned all over the world and in places where it takes a while to get there (most of the time I fail to get to a haven and defend it) even with the fastest ships available (Helios from Synedrion). Feels.....cheaty.
Also, the enemies become difficult early in the game not to mention that Sirens and Chirons can be met within the first 3 or 4 haven defenses. In my case, I had a Scylla on my 5th haven defense. Yeah, that's the level of bullshit sometimes.
In response to this you have to get in contact and ally with New Jericho for the best armor piercing weapons, with Disciples of Anu for the best shotgun and priest, with Synedrion for the paralysis sniper rifle, fastest ships, infiltrator class. Just get on good terms with all of them, but prioritize NJ. At 25 rep, they show you on the map all the havens that faction has, at 50 it shares research with you which is instantaneous, at 75 it gives you all the research and at 100 it gives you 1k of every major resource.
It really pays off to work with the factions, and if you're really desperate you can raid them for resources and tech and research. If you get lucky you can get research for weapons, vehicles, armors, ammo etc.
A cool thing you can do with your bases if they're getting attacked is to build only one access's lift. That way the enemies will come in one way instead of multiple if you more than one lift. Also vehicles are only good in the beginning, after that they don't compare to 3 lvl 7 soldiers.
Keep new recruits in bases with 4 or 5 training centers and they level up very fast.
And the last mission is hell. You need all the ammo you can carry or bring 8 priests or so (haven't tried that).
Best skills: dash, rapid clearance, rage burst, mind crush, quick aim, marked for death, reckless and others depending on class and proficiencies and various combos. Also, turrets are great.
Hope this helps.