Their main attack has 3 steps. They pose while attacking. First, they shoot 4 projectiles in a "+" shaped pattern, followed by 4 shots in an "X" shaped pattern, and finishing with another 4 shots in a "+" pattern. Their other attack shoots 8 projectiles in a circle around him.
Lokii's halves will also randomly teleport themselves during the fight and occasionally spawn a Red Boom Fly.
Try to focus on one half in order to make the battle easier. Watching for Lokii's signals can also help in predicting and avoiding their attacks.
Eternal Lokii is exactly the same as Eternal Loki.
From the artbook at page 10, Lokii's appearance from the top right is identical to his normal counterpart, but the only exception is that he possess with bat-like wings, meaning that he wasn't a posthumous version at all.
The two 'i' letters at the end of Lokii's are likely a reference the Roman numeral II, which is 2, referencing the fact that Lokii is just Loki split in 2 halves. This gets supported by the way the name is written on the vs. Screen: The two i at the end of the name have a straight line through them at the bottom; such lines are commonly added at the top and the bottom of the letters when writing a Roman numeral.
He is even more infrequent and rare to find than regular Loki; to the point that he was thought to be bugged out of the game until his appearance was reported a couple of weeks after the release of WotL.
Despite obtaining Lokii's two pair of arms from the in-game of Rebirth, his arms are still missing from his "Vs" artwork.
Magdalene vs. Lokii - TBoI 1.333 Petden
The Binding of Isaac Wrath of the Lamb Bosses Lokii (Blind)