if I have Hida Ikarukani in a battle against a personality that has been targeted by the last one, if Ikarukani is destroyed would the last one personality be destroyed by Ikarukani's trait as it is not targeting..?
trait destruction vs the last one
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
if I have Hida Ikarukani in a battle against a personality that has been targeted by the last one, if Ikarukani is destroyed would the last one personality be destroyed by Ikarukani's trait
Yes he would be destroyed, assuming he is unbowed and alone in his controller's army. The Last One negates effects of other players' actions that would destroy its performing Personality. Here the destruction is an effect of another player's trait so The Last One will not negate it.
as it is not targeting..?
It does not matter in this situation, no reference is made to targeting in the text of The Last One.