Hello everyone. I felt the need to do this since unlike Runes, Relics get new additions once in a while, and it'd be a chore to update every single one of my analyses just to add said Relic to my list of options. Instead, I will analyse every respective Relic here and tell in which situations or on which kind of monster they'd be useful on so that you may experiment more freely and I may relieve myself of the need for updating my past analyses.
Before beginning, I must mention that some Relics are obviously weaker than others and some Relics are not useful at all. To more effectively show this, I will list the higher powered Relics before those inferior ones so that you can know the one below is weaker than the one above, but can sometimes be used as a substitute if you don't have access to the latter.
Essences focus almost exclusively on healing allies, and in this regard they're similar to Shields and Armors. However, healing can't protect monsters at full health like Armors can, so they're inferior to them in that aspect. Still, there are some great Essences out there, plus they are still good at keeping your monsters alive in their own way.

Essence of Xiron: This Essence aims solely to fight Stamina Drains and high Stamina costs. Having 3 uses of this means that Stamina Drain probably won't be a problem. Because it works when the turn starts, monsters with extra turn attacks can use one when their Stamina is low to activate it, thereby removing the need to eventually waste a turn to recharge.

Yamada's Essence: It's one of the more generally useful Essences. A very straightforward Relic, Yamada's Essence is good to protect your monsters in wars of attrition, but it's risky against powerful attackers if their AOE wipes your allies out in one go.

Uriel's Essence: Revival is invaluable in this game, making Uriel's Essence one of the best Relics one can have on their monster.

Comeback Essence: Inferior Yamada's Essence. Notable absence of a Life check.

Great Healing Essence: Inferior Yamada's Essence. Heals all allies regardless of their Life.

Major Regeneration Essence: You want your monsters to be alive, not dead. Skip.

Major Healing Essence: Inferior Great Healing Essence that instead checks if any ally's Life is below 50%.

Major Vitality Essence: Too unpredictable, skip.

Regeneration Essence: Inferior Major Healing Essence that heals only the wearer earlier than said Relic.

Last Health Essence: Inferior Major Regeneration Essence.

Restoring Essence: Inferior Major Healing Essence.

Healing Essence: Similar to Regeneration Essence.

Vitality Essence: Inferior Major Vitality Essence, but it at least always gives Life to the wearer.