To start out, refer to the image if you're unaware as to Umbra's whereabouts. The quickest way, as it should be noted that this ONLY works as an Argonian, is to swim across from the Imperial Waterfront. If you're on max difficulty, make a beeline to the dungeon's entrance. If not, feel free to kill whatever enemies spawn outside.

The beginning of the dungeon can be tricky on max difficulty as pretty much anything can kill you in a matter of hits, especially the rats which seem to home in on your character no matter what you do. Make a save before you proceed further than the entrance of the dungeon as it is likely you'll die a few times trying to bait the rats into the spike trap located in the center of the first room. The goal is to get all three rats on the trap platform and leap off of it before it descends. This will instantly kill them and allow you to progress to the next area. This area is much easier, simply run to the floor grate and watch as everything around you dies to the poison mist it spews.

This mist is what enables this strategy, and is why we must be an Argonian as they are completely immune to poison.

Just beyond the poison grate is the room where Umbra resides next to her campfire. She won't attack until you do, but even on the easiest difficulty she's a tough fight at level 1. Because of this, we aren't going to fight her at all. We're going to use the power of our words and the incredibly lethal effect of the poison grate to murder Umbra without so much as drawing our weapon.

We start by pick-pocketing her so as to bait her into walking towards us. We'll run all the way to the poison grate and wait for her to get in range. You'll know she's in range when she starts making pain noises. Once her chorus begins, we'll initiate dialogue so as to trap her in place and literally stare at her until she dies. It's important you don't leave the dialogue screen as she'll walk back into her room and you'll have to reload a save to bait her again. It'll take a few minutes, but eventually she'll succumb to the poison and you'll be free to loot her corpse.

You did it! You cheesed Umbra just as Godd Howard intended! Enjoy your newfound rewards and be sure to flaunt that Argonian Superiority like the sexual tyrannosaurus you are!

Credit to demoh2o for providing the basis of this strategy.