The Destiny 2 Umbral Incursions, Umbral Flames, and Umbral Infiltration Stasis quests were famously grindy when Destiny 2: Beyond Light was first released, but they've since been toned down. That said, these quests still take a bit of doing, and they're essential to maximizing the Stasis toolkit, so it's worth doing them as quickly as possible. With that in mind, here are some tips and strategies to help you clear these quests efficiently.
The Exo Stranger lets you choose between Vanguard, Crucible, and Gambit quests when unlocking Fragments, and we'll be focusing on the Strike-focused Vanguard quests here. There are a few possible variants, but they all share objectives ranging from killing Champions with Stasis damage, getting Stasis ability (Super, melee, or grenade) final blows, or defeating combatants slowed by Stasis. Players have reported some inconsistencies with these objectives, and it's possible that there's a bit of bug interference, but we've found several ways to speed them up.
Speed up ability kills with the right gear and Exotics
One huge tip is to use Traveler's Chosen, the Exotic sidearm that replenishes ability energy, if you have it from last season (if not, find it in the new Exotic kiosk in the Tower). This will dramatically speed up all Stasis kills, no matter your class or build. You can also use Salvation's Grip, the new Exotic grenade launcher in Beyond Light, for shatter kills, but it will not count as an ability kill. Salvation's Grip also does very little damage on its own, so think of it as a setup weapon rather than a finisher.
If you have a full team, run Blind Well for the fastest kills possible
Some quests require you to run through the Strike playlist, but these Umbral quests are generally open to any Strike, meaning you can load up a specific strike on a destination. This is especially helpful if you have two friends to play with, as you can then load into The Corrupted Strike in the Dreaming City and, rather than playing through the actual Strike, travel to the Blind Well and kill enemies there. The Blind Well is full of squishy enemies and its orb mechanic gives you functionally infinite Supers, so it's perfect for any ability grind. However, everyone in your fireteam will need to be on board with the plan, as playing the Strike normally will pull everyone forward.
Get faster Champion kills with precise abilities and checkpoints
For Champion kills specifically, you'll need to head to the Nightfall on Hero difficulty (1220 Power) or higher. You don't need to be 1220 Power to do the Nightfall, nor do you need to be in a fireteam, but you should aim for the soft cap of 1200 Power to make things easier. This strategy will work regardless of the current Nightfall Strike, but you'll need to tailor your loadout accordingly.
Be sure you have suitable anti-champion mods unlocked on the seasonal Artifact and continue with the Strike until you reach a checkpoint for an area with Champions in it. From there, damage the Champions until they're at low health, hit them with a Stasis ability until they're frozen, and then kill them with a finisher. As long as Champions are under the effects of Stasis when you finish them, killing them this way guarantees Umbral quest progress. After that, it's as easy as letting enemies finish you off to reset the checkpoint.