Ignore the listed stats as they don't count [Critical Precision]'s 500% bonus crit chance and don't account for the ridiculous new headshot multiplier combined with the additional 30% headshot damage bonus of [Primary Deadhead]
Unstoppable slash damage monster that abuses the new mod [Critical Precision] to [Reach] an insane 224% crit chance overall thanks to the combined 700% bonus crit chance from both [Critical Precision] and [Critical Delay].
This setup absolutely shreds everything aslong as you can land a few headshots at the start of each mission to scale up [Critical Precision]. After that you really don't even need to aim for headshots unless you end up losing stacks to misses as the damage is more than enough at that point. You'll also naturally get a few now and then to maintain [Primary Deadhead] stacks without any effort.
[Critical Precision] - The star of the show. 500% bonus crit chance the entire mission with no time limit that's effortless to maintain.
This mod is extremely easy to stack up as multishot counts towards its stacks meaning every click at the start of the mission will give you 60-90% bonus crit chance and you'll [Reach] 500% in seconds. It's also extremely hard to lose as you only need to land a single bullet from each burst to avoid losing any stacks, and even if you miss a burst you only lose 100% of the bonus which you regain instantly anyway as soon as you land another headshot.
Possible the best weapon exclusive mod in the game now.
[Hunter Munitions] - With at least 100% crit chance, the average burst fire is going to proc multiple times guaranteed leading to huge amounts of slash procs and making armour effectively not an issue for this weapon. The slash procs scale with the headshot multiplier and the massive crits leading to even the toughest grineer in steel path dying to a single headshot burst.
Against corpus and infested you could potentially swap this mod for an elemental mod effective against either shields of infested health as while it still does alot of damage, that damage doesn't matter if you can instantly kill whatever you shoot anyway. This isn't necessary most of the time as it still absolutely shreds both factions well into steel path even without any substitutions, it's just a potential extra bonus if you wanted.
[Bladed Rounds] - What use is crit chance if you've not got the crit damage to back it up? This mod is easily substituted by any riven with critical damage attached and leads to a stronger build overall. Without a riven it's the best bet as it puts in alot of work when you're getting guaranteed orange crits with a 25% chance for a red crit.
[Primed Shred] - Punch through is almost essential for a single target weapon like the [Tiberon] and firerate is a great thing to have too. There's really no perfect replacement for this mod unless you get firerate or punch through a riven, then I'd suggest swapping [Vigilante Offense] or [Vigilante Fervor] as needed.
If you do not have this mod, regular [Shred] will suffice just fine, however you will notice an impovement when you can eventually swap it for the primed version.
[Galvanized Aptitude] - This mod works well with the [Tiberon] primes naturally high status chance and burst fire. Extra chances for slash procs add well to DPS against grineer and it gets even better if you run elemental damage either through a riven or through substituting [Hunter Munitions] when facing corpus to add extra status types.
I also highly recommend running [Panzer Vulpaphyla] as it applies viral to everything constantly which increases your slash proc damage and raw damage massively AND buffs [Galvanized Aptitude]'s direct damage buff.
(https://overframe.gg/items/arsenal/646/stabilizer/) - This mod combines with [Primary Deadhead]'s recoil reduction to leave you with -100% recoil, making this weapon a perfect laserbeam of death.
Why I don't run faction mods:
Simple answer? You don't need them. The damage and subsequent slash procs are more than enough to kill any enemy in a single burst without bane mods so they end up not actually contributing to ammo efficiency or kill time outside of extreme cases, and even then they only speed things up a little. Personally I don't think it's worth the effort to swap them out each time as this weapon really does fine against all factions without changing anything.
If you really want to, you can swap [Galvanized Aptitude] out for a primed bane mod of choice, it will be stronger but you won't notice it in anything other than a steel path endurance run as it's extremely overkill for any other content.
Generally speaking Critical Damage is the absolute king, it's not worth running a riven if it doesn't have it IMO.
Outside of that I'd suggest the order of Critical Damage >>> Elemental Damage = Multishot > Status Chance = Base Damage = Crit Chance = Physical Damage >> Fire Rate = Punch Through
Example of a strong riven:
P.S. Make sure your riven has a non-crippling curse! Riven curses massively boost the bonus of the other stats, and rivens without curses are much weaker as a result. Good curse choices include -Zoom, -Impact damage and -Ammo maximum. - Faction damage is also a decent choice if you're mindful of it, especially vs infested as you will overkill infested to such a huge degree that it won't matter much if you've got some -damage vs. infested on a riven.