Well first you got to figure out what the heck is healing it. It does have a healing ability of its own, purification, in which it destroys a friendly ship and gets its health, shields and antimatter. If this is whats keeping you from killing it, you may want to try destroying the fleet around it first. If it tries to escape I think the Jarrasul Evacuator's gravity bomb can keep titans from phase jumping if it tries to flee before you finish it off, plus nano disassembler is great for weakening any tough target.
In addition, Vasari corvettes passive debuff abilities weaken the power of healing abilities on the targets they hit, and may reduce passive regeneration as well. You might want to wait until you've drained its antimatter with at least a pair of Kortuls with disruptive strikes, since Chastic burst will devastate corvettes.
Also, when you actually kill the thing, remember to get the heck out of the gravity well. When an Eradica dies, its spirit will remain behind for a few minutes and basically enter god mode. Get everything out of the way cause anything it catches will die very quickly.
That said, as Vasari Rebels killing anything should not be that hard. The Starbase is a huge advantage, and your titan is great at destroying the frigates that will let the Eradica heal. You also get the best phase missiles, which should be a huge advantage of dealing with advent.