To irradiate with triggers, you need to create an isolated enclosure. Inside this enclosure, you must pre-place a computer-controlled Cocoon with 0HP and a Raszagal Corsair. The Corsair must be attacking the Cocoon constantly. When you wish to irradiate something, create a Terran Science Vessel (owned by the same player that owns the Cocoon), move the target unit to the enclosure, and create several 1HP Terran Civilians (belonging to the Cocoon's owner) at the enclosure. The Terran Science Vessel will respond to the Raszagal's attacks by irradiating the target unit; the Civilians will die instantly from splash damage. You can detect when the spell completes by detecting their deaths.

We have a bit of documentation on this in the wiki:

http://www.staredit.net/starcraft/Spells_(Terran)#Irradiate
http://www.staredit.net/starcraft/Irradiate
It sounds like the aggressor shouldn't be attacking the Science Vessel for it to work. You can try just making a lot of Civilians (or maybe Dark Templar or something if you don't want the players to see them) underneath the Science Vessel to see if it will react when the Mutalisks attack, though. Also make sure the Science Vessel has the ability researched and has enough energy to cast the ability, of course.