So, the trick with the the Ava eye phase is not individual brute strength (although that can help to a certain extent), but rather finesse. The idea is that you finish off the eyes at the same time within a few second window, exactly like the group.
Based off of this information, the sword, dagger, and staff classes are much easier to pull off without even worrying about what abilities you have. Send as many eyeballs down to the lowest possible health, then finish them off as fast as possible (it’s up to you whether or not you want them to have slightly more health for a margin of error when missing shots aimed at different eyes, or if you don’t want to risk taking too long finishing everything off at the same time).
As for katanas, wands, and bows, the piercing requires an even higher amount of finesse. They have a harder time sticking to a single target (obviously), so a higher amount of skill is needed for an average character, ignoring abilities again.
In my experience with the piercing weapons, tiered bows are the most difficult to control with the spread. At least with katanas have the advantage of dealing a more controlled high damage (so it takes less time if you make a mistake, and you can hit individual eyes with the tip), and a wand deals low enough damage to not mess up faster than you mean to.
Every class has the potential to solo the avatar given the right equipment, but for the sake of simplicity, the worst classes I’ve found die spoiling that Ava phase have been the archer, priest, and bard. I hope that wasn’t too long and not incredibly boring; I only experimented with this when I was solo closing a Realm to guarantee a solo trip to Oryx for the Oryx Slayer bonus. (Ava still sucks )