Essential Items:

-Primer weapon
Lycath's [Hunt] builds its own Duration by killing enemies with 5+ different Status procs. So get yourself a primer that can fulfill this task for you easily. Popular options are Epitaph (recommended due to the large radius and ease of spamming shots) and Kuva Nukor.

-Melee weapon or good aim
Lycath's Hunt generates either Health Orbs (melee kills) and/or Energy Orbs (headshot kills) at a 50% rate. You'll want to be sure you can net these returns often. Melee recommendation is a [Glaive] weapon such as [Xoris] or [Glaive Prime]; it can pair with [Epitaph] or [Nukor], giving innate Blocks from incoming attacks, and the heavy detonation has forced procs and can potentially kill multiple targets, which quickly regenerates Duration for Lycath's Hunt.

Mod Breakdown:

-[Brief Respite], [Primed Sure Footed] and [Rolling Guard]
Our standardized defenses. Shieldgate (with at least one Augur mod), status cleanse, brief invulnerability and stagger immunity.

-[Blind Rage], [Umbral Intensify] and Molt Augmented
You need 200% Ability Strength to fully defense strip with Fusion Strike. The excess Strength goes into Sentient Wrath (and of lesser importance, Lethal Progeny). When capping out Augmented, you can hit up to 48 enemies with a single cast of Wrath; all affected enemies will receive a Lifted status proc (useful for Hunt) and a debuff of 106% for the Duration of the Ability. As for Progeny, well...stronger meatshields in non-level cap runs.

-[Stretch] and [Augur Reach]
This extends Fusion Strike's fallout zone to slightly over 17m, and makes Sentient Wrath hit enemies 38.5m away. If you're less concerned with using these abilities, you can consider these slots flex options (I strongly recommend not reducing your Range below 100%, for the sake of Fusion Strike; even at 10m the lingering fallout gives permanent armor strip, which will be handy for choke points).

-[Primed Continuity]
While Duration isn't as important for Lycath's [Hunt], it's just important for all of [Caliban]'s other skills to warrant at least this mod. You can also use Augur Message if you wish to drop a Range mod (in fact I'd recommend it, for sake of Shieldgating off all of your abilities).

-[Primed Flow], Arcane Energize and [Equilibrium]
[Caliban] has low Energy reserves, and with [Blind Rage] it's going to be drained even more per cast. [Primed Flow] is a MUST in order to afford your abilities; Equilibrium will synergize with your melee kills off Lycath's Hunt; and of course Arcane Energize speaks for itself.

-Archon Shards
I strongly recommend 2 Amber Shards (preferably Tauforged, but normal will suffice) for Casting Speed; Fusion Strike is a very slow ability. Your last 3 slots, I'd recommend one of two things:
1. Ability Strength to either give more fuel to Sentient Wrath, or to give yourself the ability to swap [Blind Rage] for [Transient Fortitude]. You'll lose some Duration, but your Energy economy is more important.
2. Ability Duration to further support your abilities.

-Alternative Mod Options

Augur Message -- as mentioned, you can ditch some Range if you want, but don't ditch not having at least the one Augur.

Transient Fortitude -- you'll lose some Strength and Duration if you slot this over [Blind Rage], but you'll [Recover] on Efficiency. If you take this route, make sure you have extra Augur mods on your Secondary or Sentinel so you can Shieldgate from any ability. You'll need 3 Augur mods total, otherwise you'll have to cast 4 each time.

Augur Secrets -- if you can't afford Umbral Intensify and don't want to lose Duration from Transient, this is a moderate backup.

Natural Talent -- in case you want to save your Amber Shards.