I think fighter also fits better thematical than assasin.
A assasin is usually a methotical person, planning his steps, goes in for his target and out, clean and quiet.
Non off that is true for Diana.
Diana reacts on impulse, she killed because of surival instincts and anger, not because she planned to do so and excuted it methodical.
She's more straigth forward, simply chasing enemys down and defending her self.
And thats what figthers do, the go in, they stay in, the don'T have a masterplan, they just decide on the fly.
do not mistake figthers for tanks