My guess is that that word is specifically "made up" for the game and holds a specific meaning just inside the context of that story (meaning that you won't find 氣現 in a Japanese dictionary).
I found something that might be useful here. It seems it could be related to 氣現獣 that seems to be a sort of summoning art.
Let me quote:
その名の通り、自然界に存在する「氣」の力を利用することで攻撃や治療を行う。 利用する「氣」は、水の氣、大地の氣、そして命の氣まで様々であり、
作中では巨大モンスターを投げ飛ばしたり爆発から身を守ったり、溺れたアイの命を救ったりした。
ただし、その力はまさに諸刃の剣で、氣の流れを読み違えると大変な結果を招いてしまう。
物語中盤でリサは自分の命の氣を削って巨大なエネルギー体を生み出した。 その姿はアイによって「氣現獣」と名付けられ、以降も何回か召喚している。
Maybe they are using the traditional character 氣{き} and 現{げん} together to convey the meaning of "materialization of ki" ? This is just a guess though.
So my idea is that 氣現にして could be referring to the Leviathan and be simply translated as something like "appear / come / materialize / become real".
So your translation would be
Oh blue god, born in the spring of the creation of the world! Oh
utmost god, come and purify this corrupted earth! Now inhabit my
flesh and save my tribe!
Now a couple of things: first, I'm not 100% sure as I don't know the game and I'm just guessing. Second, I realize that the English translation I gave is nowhere near as cool as the Japanese 氣現. :)
EDIT: I just realized that with my explanation I would not be sure how to account for the particle に (I missed it at first). What I said could make sense if it was 氣現して but I am not sure it still holds with に that makes it look like an adverb. I'll wait for some comments and eventually edit my answer or just remove it if it's too far off.
EDIT 2: Please disregard my answer and refer to Mackygoo's one. I won't delete mine as I think it was a good try and still adds some info.
