If you're having trouble doing this head-on, there is a stupid simple method to beat it. It's a bit tedious and takes much longer, but it's also way easier.
This method only requires soloing Kerrigan, so you can ignore the rest of her army. As soon as it starts, just tell the entire army to fire on Zurvan and then forgot about them. They will be killed off pretty quickly. Focus all your attention on Kerrigan.
The far top-left and top-right corners are dead zones that Zurvan's tentacles never hit (Falcon165o's answer provided a screenshot that demonstrates this well). The trick to make this easy is that you can burrow Kerrigan in this dead zone. In this state, nothing can hit her -- she is out of range of Zurvan's tentacles, and the minions can't see her.
And if you position Kerrigan at the very top edge of a dead zone, she is in range to hit to Zurvan. So the idea is to:
- Position Kerrigan in one of those sweet spots where she is in range of Zurvan but still in a dead zone. I used the right-hand dead zone for this, but I think the left-hand side also has a spot that works.
- Hold position and start attacking Zurvan. The minions will start coming towards you. The acid-throwing minions may hit you a few times; ignore this.
- When the minions get close, cast heal (to heal from any acid that hit you) and then immediately burrow. Make sure to keep Kerrigan in the right spot when you burrow; she has a tendancy to wander off out of the dead zone towards the minions unless you stop her. After burrowing, the dazed minions will wander off.
- Zurvan will continuously be spawning more minions but also continuously killing them with friendly fire, so it's pretty stable.
- Rinse, repeat. If at any time you feel like Kerrigan's health is running too low, you can just in rapid sequence unburrow, heal, then reburrow until her health goes back up.
That lets you beat stage 1 without even breaking a sweat. When Zurvan hits stage 2 (I think that happens at 25% life), the minions stop spawning, at which point it becomes a cakewalk. The rotating cone of fire is easy to dodge just by walking out of it (or psionic shifting in a pinch) and the little electric fire things don't hurt too much. So for this stage it's as simple as:
- Dodge Zurvan's fire cone. Heal Kerrigan if she takes any damage from those electric fire things.
- Attack and/or leaping strike Zurvan until the cone starts coming towards you again.
- Rinse, repeat.
That's it! If you're paranoid about making a mistake, save the game frequently.