What is the optimal way to defend Kerrigan in the Crucible mission?

As with all things Zerg, make sure you have enough drones to supply your economy. I took the expansion very early, which certainly helped.

As far as defending the ramps, A good mix of spine crawlers and swarm hosts up top, with roaches/zergling in front works pretty well. One other thing to note, especially on harder difficulties, is that spine crawlers and swarm hosts don't have to be static defenses. If you have a big push on one side, and not a lot defending it, walk your spines/swarms over and help defend. I didn't build up much in the way of static defenses on the bottom ramp, but had a hit squad of mutas, and some roaches near it to deal with the bit that came that direction. Don't forget some spore launchers around the bottom of the base for the flyers that come in.

If you want to also take the Tyrannozor out, I just took a ton of roaches, burrowed them, and walked them over to him. Popped up next to him, and with enough roaches, dropped him directly.

Despite what the mission encourages, I found that there was actually very little need for static defenses, opting instead for a ball of zerglings and mutalisks.

If you're not already using it, consider using Zergling Reconstitution for this mission, and try to build up 20-30 'lings (Raptors are preferable, if you're playing from the master archives) and then just start massing mutalisks.

The goal here is for your zerglings to "tank" the primal zerg, in that they delay them from reaching the Chrysalisuntil your mutas can reach the intruders and annihilate them with bounce attacks.

Building a large force of mutas also allows you to take out the Tyrannozor pretty easily - simply fly over the battling primals, and burn him down with your air units. Unlike most missions, you do not actually need a ground unit to collect the essence it leaves behind, so there's no reason to use ground units at all.

As the mission progresses, especially in the last 6 minutes, the primal zerg will stop coming in waves, and start coming in a constant stream. Make sure that before you reach this point you build 5-6 swarm hosts and root them around the Chrysalis. Between the swarm hosts themselves and the locusts they spawn, they'll form a solid "Wall" around Kerrigan that will prevent the primal ultralisks, roaches, and zerglings from melee-ing the Chrysalis. (Unlike the other units, since they can't attack air, they won't be distracted by your mutas, until they die). You can't build crawlers directly in the pool to wall off that way, but your ground units can burrow (or root!) in it just fine.

And finally, be sure to use the Locust ability of the Chrysalis as needed -- there is nothing to be earned from not using it, so use it as-needed.

One final thing to consider is that, should you find the Chrysalis has taken a lot of damage in a previous attack, you can use the abilities of your Swarm Queens to heal it.