Ok so I ended up beating it. 100%!
Heavy use of save and load. Save before Kerrigan shows up and after she retreats. If you lose too many units (like 3 BCs to Kerrigans stupid magic hand wave instakill bull), then reload.
Take out the Nydus worms as flying units are easy to deal with
Build BCs to make use of Yamato cannon on Kerrigan and the Leviathan (the giant flying guy).
Build Marines and medics; make use of stim.
Build a few Science Vessels to help with healing your BCs. Build them early.
Build, and never stop building, SCVs. Trust me, I had the research that lets me train 2 SCVs at once, and I NEVER stopped building them. You need them for repair and to keep up with the mineral gathering.
Keep SCVs near chokes to repair
Construct flame towers near the choke. If you didn't get flame towers, build a few planetary fortresses at the chokes and have a bunch of SCVs there to auto-repair (no seriously, it'll work, lots of HP, lots of splash damage).
Construct a few flame towers sporadically in your base to deal with random drop pods.
Construct Barracks at each choke point to serve as a wall between incoming enemies. This also helps keep Kerrigan back.
Get as many ship and infantry upgrades as you can. Do it early.
Make use of mind control towers. Build them early on the left and the right sides.
Use mind controls towers to grab as many brood lords and Ultralisks as you can. Broodlords are imba and you want to make use of the infinite infantry they can provide. Mind controlling Ultralisks is amazing too. Especially if you have medics there to heal them.
Build a mind control tower and turret behind your mineral line to mind control brood lords that attack from behind. Mind controlled units will NOT be affected by the nova blast (lulz)
Make sure you have mind control energy when the big ultra push happens toward the end of the mission.
Save a Nova blast for when the Leviathan attacks. It will decimate you otherwise because it constantly spawns Mutalisks and Broodlords
If Kerrigan or the Leviathan isn't around when you needed to nova blast, then it's likely that you need to reload a recent save. Though don't Nova blast too soon when Kerrigan shows up. The blast has limited range, and you want to wait for the next wave of flyers/worms that quickly follows her.
Just before the Leviathan shows up, start cranking out some vikings to deal.
The drop-pod research is useless. Get the Tech-reactor research.
If you ever lose too many key units or structures (especially in the beginning), reload from the last save. It will end up costing you the mission in the long run.
Tanks don't work so well because Kerrigan's area of effect attack can easily clean out 4-5 tanks and there's not much you can do. This makes units like BCs more cost effective because they can get out of the way.
Buildings work great at attracting Kerrigan's focus. She will spend her energy doing an AoE to the building and not doing it to your units. Also, keeping a building alive is much easier against her because they have tons of HP and huge surface area to repair
Don't use supply Depots at your choke. They do not have enough HP or surface area to repair. You aren't going to leave your base anyway (not with units that don't fly that is...)
Best Answer
Abuse blink stalkers like crazy, blinking back the hurt ones as soon as they lose all of their shields during fights. After the second part, bring your Stalkers along as best as you can, but don't really worry about them and don't even bother trying to fight. Just run/blink by everything, with a special focus on keeping Zeratul as healthy as possible and not getting blocked or stopped at all. It might take a few tries, but for me it was one of the easier missions on Brutal.