Han Solo must ignore taunts with his first shot, he is useless at the moment.

Han Solo's shoot first is a counter to speed teams.
Ignoring taunts should be basic to his ability, or at most Omega.
Shoots first should have an overhead icon and be an undispellable buff.

Zeta should give him +% potency, dispel all enemy buffs and increase damage per buff dispelled, and inflict Buff Immunity to the enemy as well. A killshot by Han should give him the "Shoots First" buff again - this buff regain would pierce any debuffs, like buff immunity.
In the future, another version (non-clone wars) Chewbacca would sinergize with him, and killshots by Chewie would grant him another "shoots first" buff as well.