Eidolon hunting with [Wisp] is possible. She's a versatile frame that can act as a support but also as the main DPS against the Eidolons.
This build considers that you know how [Wisp] works so we won't explain the mechanics here (for that there's my other [Wisp] build, check the profile to find it).
With this build you should be able to heal the lures if you are the caretaker thanks to the [Vitality] Mote. But you will also be able to deal a very high amount of damage thanks to the new augment. When you have to shoot the Eidolon just use Breach Surge to teleport to one of your motes, increasing your Critical Chance while doing it. The high power will allow you to need less traveling distance from where you are to your mote in order to cap Critical Chance so you could just cast a reservoir move a few meters and then teleport. You'll have CC maxed and ready to shoot with your sniper.
By adding Eclipse you further increase your damage dealt. This ability however, can be switched with [Oberon]'s smite, but you'll need the augment mod, so think carefully what you want to remove. I suggest [Augur Secrets].
Reservoirs are static, so it is important to keep refreshing their position according to your party location.
Arcane Nullifier is a must in this Eidolon build to counter the magnetic procs from the shockwaves.
It goes without saying but this build requires a Sniper Rifle for the [Hunt].