Call 130 : Fusion

朧、その時
別なるモノにーーー
That was the moment when Oboro turned into another kind....

I would replace another kind with something else.
That was the moment when Oboro turned into something else...

朧『悪いが・・・実力は君より上だ』
オド『・・・・・・！！』
朧『喋れない戦士か　それなら好都合・・・　僕はこの世界ではまだ誰でもない　だから僕が君になってあげよう』
オド『！！！』
Oboro : What a shame.... but I'm stronger than you!
Odo : ......!!
Oboro : A warrior that can't talk? ...That'll be a good opportunity for me... I'm still nobody in this world, let me become you!
Odo : !!!

A warrior a person, not a thing. So "who" instead of "that". I would make this a little more succint. Shorten it to "What a good opportunity..." or "What a good opportunity for me...". Also, no one from nobody, so the singular subject agrees with the singular noun ("I'm" is a single subject. "Nobody" is plural where as "No one" is singular). So it reads, in the end:
Oboro: A warrior who can't talk? ...What a good opportunity... I'm still no on in this world, so let me become you!

デルボロＶＳ朧・・・
デルボロ『オドを殺しＷ・Ｉ・Ｓ・Ｅに潜入するとはな　お前一人でどうするつもりだ』
朧『潰すのさ』
Delboro vs Oboro
Delboro : You invaded into WISE by impersonating Odo.... but what can you achieve alone against WISE!
Oboro : Crush it.

In this instance, "into" is unnecessary. Also, you can use achieve, but I think it's a little over the top. "Do" makes it shorter and means the same thing. Also, this is a question, not a proclamation, hence the "?" rather than "!"
Delboro: You invaded WISE by impersonating Odo... but what can you do alone against WISE?

上半身裸の朧・・・
デルボロ『・・・・・・！？　何・・・！！』
朧『君なら僕の体を見てわかるだろう？』
Oboro bared his upper body...
Delboro : ......!? What...!?
Oboro : For someone like you, you know what this means when I show you my body right?

This is just an awkward statement by Oboro. I don't want to completely reword it, though, so how about this...
Oboro: Because it's you, you understand what uncovering/showing my body means, right?
Uncovering, showing, either one works, so take your pick.

体中にイルミナが・・・
朧『僕と君の間に広がる　圧倒的な力の差が』
デルボロ『なんだその数のイルミナは・・・！？　馬鹿な・・・！！何故生きている・・・！！』
朧『それは僕が天才だからだ　天才望月朧は　死んでも生き返るんだ』
His body with (full of?) Illumina...
Oboro : There a overwhelming gap between us...... in our powers!
Delboro : What's with this number of Illumina...!? How can.....!! Why's he alive at all...!!
Oboro : Because I'm a genius - Mochitsuki Oboro the genius... becomes back from the dead!

"An" instead of "a", because overwhelming begins with a vowel, "o". "The" number of Illumina instead of "this". "Becomes" should be "came". It already happened, past tense.
Oboro: There's an overwhelming gap between us... in our powers!
Delboro: What's with the number of Illumina...!? How can...!! Why is he alive at all...!!
Oboro: Because I'm a genius. Mochitsuki Oboro, the genius... came back from the dead!

巨人ＶＳカイル・・・
カイル『がはッ・・・！！』
Giant vs Kyle....
Kyle : Kaba...

吹き飛ばされるカイル・・・
カイル『おおおおッ』（フーを助けなきゃいけねえのにッ！！）
Kyle blown away...
Kyle : Ooooooh (I was supposed to be helping Fu by now!!)

壁に穴が開きそこからデルボロと朧が・・・デルボロ胸に大穴・・・
デルボロ『か・・・！』
A hole opening up in the wall.... Seen from that hole was Delboro, sustaining a huge hole at his chest....
Delboro : Ahhh...!

朧（禁人種の墓場に沈められた僕に出来たのは　自分を治療することではなく　イルミナの力で生命を作り変えること）
朧（堕ちる処まで堕ちた　あとは登りつめるのみ）
Oboro: The one thing I managed to do back there at the cemetary of tavoos
was not to cure myself, but to create alive out of Illumina )
Oboro : (Falling from where I have fallen, the only way to go was up!)

Lordy. Let's put this all in the same tense, shall we? I think we can leave out "back there", it's unnecessary. I'm not entirely sure what "create alive" means, but "be reborn from" sounds better and works in this case. "Falling" can be left out - it's already been established in the sentence that Oboro has fallen. Also, "had" instead of "have", as this is past tense.
Oboro: The one thing I managed to do at the cemetary of tavoos was not to cure myself, but to be reborn from Illumina.
(From where I had fallen, the only way to go was up!)

上空？のジュナス・・・
ジュナス『！！？　デルボロ・・・？』
From the sky Junas...
Junas : !!? Delboro...?

朧（この新しき力　生命融和で）
Oboro : The new strength, Live fusion 生命融和

Perhaps "my" instead of "the"?[b]
Oboro: My new strength, Live Fusion.

倒される巨人・・・
カプリコ『あー！！　ギーガー０１号！！！』
Giant falling....
Caprico : Ahh!! Giga 01!!!

カイル『あんた・・・！！』
朧『たった二人でよくやってくれた・・・　後は僕に任せろ』
Kyle : You...!!
Oboro : What achievement considering there's only two of you.... I'll handle the rest!

[b]"An" in front of achievment.
Oboro: What an achievement, considering there's only two of you... I'll handle the rest!

巨人の首筋に両手を・・・
ギーガ『！！？　ギュアアアア』
朧『生命融和』
Grabbing the giant at the hand...
Giga : !!? Gyuaaaaaa!

カプリコ『どうしたのギガちゃん！！？』
Caprico : What happened Giga-chan!!?

朧『細胞隔壁破壊・・・　そして融合　禁人種を吸収し　己の力として操る　これが頂点に立つべき者の力だ』
Oboro
: Cell wall destruction.... Then fusion! With that I can absorb the
tavoo and use it like my own powers. And that the powers something
standing on top should own...

You could probably leave out "wall" and just have "cell destruction". I really don't like this statement construction. Not sure how much I should change it around. Argh.
Oboro: Cell destruction... then fusion! With that I can absorb the tavoo and use it as my own power. [OR: With that I can absorb the tavoo and use its power as my own.] And this power is something someone standing on the top should own...

仲間割れを始める巨人・・・巨人が合体？・・・
カプリコ『ギーガー０１号！！０２号！！０３号！！　みんな助けないと　やられちゃうー！！！』
ジュナス『禁人種の体は取り込まれるだけだ　さがってろ　カプリコ・・・！』
カプリコ『ダメ！！　ジュナスの体は汚染されてるのにあんなトコに近づいたらメー！！！　あんな奴　私の力で倒せるもん！！』
Giant crumbling.... And giant fusion? ....
Caprico : Giga 01!! 02!! 03!! If everyone don't join you'll all be beaten down!!!
Junas : He's just absorbing the tavoos! Back down, Caprico...!
Caprico : No! Junas has been poisoned, you can be going near there!! Someone horrible like that, I'll defeat with my powers!!

"Don't" should be "doesn't". And "down" could be left out. It should also be "you can't go near there". I mean, Junas, you've been poisoned, listen to the woman! XD
Caprico: Giga 01!! 02!! 03!! If everyone doesn't join, you'll be beaten!!!
Junah: He's just absorbing the tavoos! Back down, Caprico...!
Caprico: No! Junas has been poisoned, you can't go near there!! Someone horrible like, I'll defeat with my own powers!!

イルミナの玉から別の禁人種を・・・
カプリコ『創造！！』
From Illumina comes other new tavoos...
Caprico : Create!!

周囲のパイプラインなども取り込む新禁人種・・・
カプリコ『よぉーし　いッけー！！！　マグマグ！！！』
From surrounding pipeline comes other new tavoos...
Caprico : Good! Go, Magamag!!!

カイル『何だってんだ・・・！』
Kyle : What just came out...!

Perhaps "something" instead of "what".
Kyle: Something just came out...!

朧『面白い・・・！！　いいだろう　どちらが禁人種の王か証明してやる』

朧『全ての力を利用して・・・！！　僕はこのまま頂上までいく　この望月朧が天戯弥勒まで辿り着く！！』
Oboro : Interesting...!! That fine, we'll prove here who's the king of Tavoos!
Oboro : Using all powers...!! I'll overcome all to the top, and Mochitsuki Oboro will challenge Amagi Miroku!!

Oh, Oboro. "That" should be "That's". Could leave out "here". Insert "my" in front of of "power". Could also leave out "all to the top", change it to "everything" or "everyone".
Oboro: Interesting...!! That's fine, we'll prove who's the king of Tavoos!
Oboro: Using all my power...!! I'll overcome everything... and Mochitsuki Oboro will challenge Amagi Miroku!!

はじける星空間・・・
チチ『完成です　行きましょう』
Star Space opening up...
Dad : It's done, let's go!

倒れこむ飛鳥・・・
チチ『く・・・！！　ゲホッ・・・　ゲ・・・！！』
アゲハ『親父・・・！！』
Asuka collapsed...
Dad : Ku...!! (Cough)...!!
Ageha : Dad..!!

チチ『あなた達がノヴァを習得できるようギリギリまで時間を引き延ばした結果です・・・！！　もう時間が無い・・・　私を置いて行って下さい・・・！！』
Dad
: It's just a side effect from stretching the time available to the
max for learning Nova...!! Time is running out.... Go without me...!!

チチ『アゲハ・・・　雨宮さん・・・　あなた達二人に未来を賭けます・・・！！』
アゲハ『おう！！』
雨宮『はい！！』
Dad : Ageha... Amamiya san.... We'll stake our future to you two...!!
Ageha : Oh!!
Amamiya : Yes!!

There should be a hyphen in "Amamiya-san". It should be "on" instead of "to".
Dad: Ageha... Amamiya-san... We'll stake our future on you two...!!

行け！！
仲間の許へ！！
Go!! To your Nakamas!!

[b]You could, I suppose, leave it as nakama. But it doesn't have to be plural. Nakama already means "friends", plural.
Go!! To your nakama!! [OR: Go!! To your friends!!]