This is my favorite Setup for hunting Eidolons, hence the Radiation.

This build heavily relies on [Depleted Reload] to work, as it doubles the effectiveness of Primed Chamber, and thus puts this weapon over 250K DPS (this calculator doesn't calculate Primed Chamber's dps correctly) and with a godly Riven over 500K DPS.

Options:

(BEST -> SECOND BEST -> ETC)
Split Chamber -> Galvanized Chamber -> Charged Chamber -> Any Element Mod
Vigilante Supplies -> (Primed) Sniper Ammo Mutation / [Stabilizer / Twitch (up to preference)
Galvanized Chamber can technically double total DPS, but is hard to keep up during Eidolon [Hunt], since it requires constant kills.

Riven

Serration is a good mod to replace with a good riven, or the elemental mods, should your riven come with those elements
I have a fairly mediocre Riven with +dmg +multi +status and -mag, best stats to shoot for:
Crit Damage > Crit Chance > Multishot > Heat/Electricity > Damage > Reload Speed > Status Chance

Good curses are:
-mag -firerate -zoom
As they don't impact performance or handling

Arcanes

DPS can be increased quite a bit with the use of Arcane Momentum and Theorem Demulcent with the latter being a bit more difficult to setup
Fractalized Reset could also be used, but Primary Merciless is generally better.
Using either Arcane Momentum or Fractalized Reset kind of requires Ammo Mutation of some sort or Ammo Consumables.