Riven-free, Anti-Eidolon, 4 Forma [Rubico]
[Rubico Prime] is currently the best sniper rifle in the game, boasting incredible Critical stats and Damage while still having good firing rate, status and more than 2 shots in the magazine.
Mod Explanation
Split Chamber: Staple in any primary, no explanation needed, huge damage boost.
Serration: Also a must-include mod, with one exception - [Chroma]. Otherwise not using this mod is like cutting your arm off. No explanation needed.
[Point Strike] + [Vital Sense]: [Rubico Prime] is a Crit weapon, and these are crit mods. And since we won't be doing much headshotting and killing anything other than eidolons (ideally) with this, we don't have other alternatives.
[Stormbringer] + [Hellfire]: Elemental mods, The two together give you a x2.8 damage multiplier (essentially) and make that damage Radiation. Radiation has a huge damage multiplier against alloy armor. Eidolons have Alloy armor. 2+2=4 and the Eidolon is dead.
[Heavy Caliber]: Tons of Damage, This is basically an extra [Serration] with a downside, mitigated by [Rubico] being a Sniper rifle.
[Vigilante Armaments]: While it stacks additively with [Split Chamber], this is still a good mod, as it increases your damage multiplicatively with [Serration] and elemental mods. It's not a huge boost, but it does end up being a chunk. Best 8th mod available IMO.
Alternatives
[Serration]: If you're using [Chroma] you may want to consider replacing this with an elemental mod, due to [Serration] stacking additively with Vex Armor, [Primed Cryo Rounds] or [Wildfire] would be my recommendations
[Heavy Caliber]: If you're getting rid of [Serration] and still have this mod in, just use [Serration] instead of this. Otherwise, consider replacing this with more elemental damage mods like [Primed Cryo Rounds], [Wildfire] or [High Voltage].
[Vigilante Armaments]: If you're open to changing your playstyle up... A LOT, consider replacing this with [Proton Jet]. I know, sounds janky AF, but it CAN work.
Exilus Slot
Personally I chose [Twitch] Because when hunting eidolons I prefer to play as [Trinity] and I take shooting down the acid orb things as my responsibility, [Twitch] helps me to switch to my secondary and take down the orbs faster.
Another good choice is [Stabilizer] as it can improve your practical DPS by making you feel more comfortable at shooting faster and makes recoil control easier.
On the Forma/mod rank note: I wouldn't bother formaing for such a minor upgrade, thus my [Twitch] is Rank 1, but if you want to use [Stabilizer] or don't have anything better to do, you won't regret putting another forma in.
The end
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