Tinasha's Mastery is the newest rocket-assisted sidearm to drop in Destiny 2, and if you played around with Indebted Kindness from Warlord's Ruin, The Call during The Final Shape, or more recently, Aberrant Action in Echoes, you'll know these weapons are a big deal. Tinasha's Mastery is the first stasis rocket sidearm, and in what is basically a stasis-focused season in terms of ritual artifact perks, it's got some wild synergy.
Most notable, perhaps, is that Tinasha's Mastery can get Chill Clip. That's right, a perk that was previously confined to rocket launchers, sniper, and fusion rifles, is now available on a fast-firing sidearm with far larger mag capacity. It's no wonder everyone is losing their minds over it. Rocket sidearms are generally a preferred PvE weapon, but here I'll run through the Tinasha's Mastery god rolls for both PvE and PvP.
The best perk you can get on Tinasha's Mastery is undoubtedly Chill Clip, so these are the rolls you'll want to keep no matter what else you get. However, if you're hunting the god roll, then Loose Change seems the way to go. This perk improves reload speed, aim assist, and movement based on applying elemental debuffs, which you'll be doing all the while with Chill Clip—the perfect synergy, really.
Air Trigger could also be pretty good, massively boosting ammo reserves. While Chill Clip is the winner, One for All is also a strong damage perk on these explosive weapons, especially if you manage to get it with Reverberation, so these might be worth keeping around.
Generally, your goal with the magazine is buffing its size so you get more Chill Clip shots, so I'd recommend Appended Mag and then Extended Mag, though you will take a hit to reload speed for the latter. You can compensate for this a little with a Reload Speed masterwork. Finally, I'd suggest Quick Launch for Launcher Barrel to buff velocity and handling, making the rockets you fire faster and the gun even smoother to use.
As mentioned, rocket sidearms aren't really a weapon that you'd often use in PvP, since you'd be sacrificing a shotgun or sniper rifle in order to bring it. There are worse weapons, though, and since it's an Iron Banner gun, it also gets the Skulking Wolf origin trait that lets you disappear from the radar.
Since velocity is important in PvP, I'd recommend Impulse Amplifier and a velocity masterwork, and then either Adagio or Desperate Measures. The former is the best with a 30% increased damage buff when you get a kill, but Desperate Measures could also work if that's what you roll. Surrounded is also a potential option, but it's worth considering you'll have to get real close to enemies for it to activate, so you're better off with Adagio if you have it.
Despite Chill Clip being strong in PvE, I wouldn't really recommend it here due to the scarcity of special ammo in PvP. Lastly, I'd suggest Hard Launch for its massive velocity boost and High-Explosive Ordnance for even more velocity and blast radius, since mag size matters little when you have basically no ammo. Quick Launch could also be a pretty good barrel option since extra handling is always nice to have in the Crucible.
