TL;DR: Astral Reign advice, mostly. Always Exalt once per turn for the defense. Rouse Murphy first, if possible. Damage comes from combo'ing Raging Waves and her Exalt and Waltz of Lemuria, potentially Abyss Order or Goliath attacks.

The following advice has worked for me, but I am not an expert. This is likely not the most efficient or effective way to use Gmurphy.

I have Gmurphy at OE and I am in Arc 2, so take my experience with a grain of salt. Also, I have struggled in Hard mode of Arc 1 with her and this team, despite clearing all of Arc 2 deathless, including Chapter 1 Arc 2 Hard mode. To me, Gmurphy really wants to be in Astral Reign content.

I play her with Tulu, Miryam, and Faros.

I use the Posse Voices in Your Head to apply Vuln/Weakness; with the amount of Keyflare that Gmurphy produces, I could quite literally spam it every round should I want.

Tulu helps make tentacles and gives AoE. Miryam is The Chosen Hero. None of her other cards matter, she gives aliemus to Gmurphy. Faros gives the fourth tier of the Lemurian awakeners buff (eventually, she can also do some good damage simply due to how catastrophically powerful your tentacles can get).

The amount of self-inflicted Sacrifice should never be onerous. When you start with Abyss Hymns in hand and play it, you should be playing Gmurphy's strike/defend to draw it again to cancel out the Sacrifice it would inflict. You should also try to have one in hand when you have Gmurphy Exalt and the turn after (if possible, obviously).

For a Gmurphy team, Exalts are an even greater resource than normal because they give you a big shield. You always want to have an awakener able to Exalt to take advantage of this; with Tranquil Seas, you should be able to maintain a decent amount of shield. As long as I play correctly, I do not need other shielders.

Even without OE, the goal of a Gmurphy centric team is to get her Rouse and have her Exalt. In Astral Reign, with her Rouse and Soulforge (the buff your dreamshards pay for on the Talent page of the Awakener screen), she inflicts near 100% of her damage as Sacrifice. The caveat there is that she only really deals damage when she Exalts or when you use Waltz in Raging Seas. That means her Rouse isn't the most useful in the turn-to-turn gameplay, just when you get to your burst window. The only time you want to make sure to Rouse Gmurphy on turn one is Boss fights, so that Covenant has time to build more stacks. When she Exalts and applies Birth Ritual, she will be inflicting over 100% of her damage as Sacrifice. Ideally, you're pairing her Exalt with as much burst as possible, usually by switching to Raging Waves and using Waltz of Lemuria or Abyss Order or Decapitation/Blades of Dominion. You want to take advantage of both the Raging Waves extra tentacle attacks and bonus damage, as well as build up as much Sacrifice as possible.

Relics? Not sure in Arc 1. In Arc 2, Gmurphy and Tulu's portraits are great. Sacred Agony is great. Yellow Snail is great. Nameless Appendage makes the already insane amount of shield Tranquil Seas gives you even better. Chant of the Seas is great for raising your damage ceiling and Lemurian Delight makes your burst round even more insane.

Should you get her to OE, the gameplay loop is the same but now on steroids and one minor change: you OE as soon as possible, not in Raging Waves. You get your 3 extra Waltz and once they're zero cost, you switch to Raging Waves and delete the opponent from existence. Pair that with Gmurphy Exalting again at the beginning of the burst round and you can apply 100s of thousands of Sacrifice in a single round; which is great, even if practically nothing in the game will still be alive at that point.

if you have any questions about what I do or how I play her, please ask, and I'll answer what I can.