What's required to save Captain Kirrahe on Virmire?

Solution 1:

Kirrahe will survive if you take out the geth fliers by disabling the landing strips on your way into the compound.

If you don't, he will die to an air assault.

How much of his team survives depends on what Shepherd does with the Alarms when entering the facility - the renegade option means less will survive, but "how much" of his team survived doesn't get carried over.

The wiki has a little more.

Solution 2:

it doesn't matter who you choose to go with the stg team as long as you disrupt communications, destroy the satellite uplink and kill the geth air drones He'll live