Timestamps
This guide is meant to provide an idea of how to get the trifecta achievement done in Veteran Vateshran Hollows by explaining the mechanics of all bosses that must be killed to get it and showing the (as to what I found) fastest and easiest order of doing the arenas.
0:00 Introduction
Hunter's Grotto
4:11 Trash up to Lurcher Triplets
5:50 Lurcher Triplets Boss Fight (Rofsuta, Saagranth & Marbana)
Finishing this boss unlocks grapple bow to access the Essence of Mysticism!
7:12 Trash up to Minotaur Boss
9:05 Minotaur Boss Fight (Rahdgarak)
The Wounding
11:15 First Trash and Essence of Mysticism (Maximum Magicka Buff)
13:32 Second Trash up to Chillfiend and Abonimation Boss
14:25 Chillfiend and Abomination Boss (Zakuryn the Sculptor)
Finishing this boss unlocks wounding portals to access the Essence of Fortitude in the Brimstone Den!
15:44 Wounding Portals up to Titan Boss
19:01 Titan Boss (Iozuzzunth)
Brimstone Den
20:52 First Trash and Essence of Fortitude
22:49 Second Trash up to the Magma Queen
23:57 Magma Queen Boss Fight
Finishing this boss unlocks the Brimstone Orbs to access the Essence of Endurance in the Hunter's Grotto!
25:10 Brimstone Orbs up to the Dremora Boss
28:00 Dremora Boss Fight (The Pyrelord)
Last Boss
30:35 Final Boss Fight (Maebroogha the Void Lich)