Oh no, here I go correcting things again. Now that I'm back, I'm going to end up completely taking over this section of the forums, aren't I? Oh well.

http://www.animelyrics.com/anime/utena/rguswkst.htm

薔薇の刻印に より選ばれし我ら
世界の果ての 手紙に従い集う我ら
チャンスを与えられた デュエリスト
決闘に勝ち 手に入れるのだ
薔薇の花嫁

Current translation:

We were chosen instead of the rose's carved seal
We assemble and comply with the letter of the end of the world
Duellist has given us a chance
She will obtain the victory of the duel Rose Bride

My translation:

We who have been chosen by the Rose Seal
We who gather in accordance with the letters from End of the World
Each of us duelists, given a chance
The victor will obtain her:
The Rose Bride

Why it's wrong:

In the first line, since it's により and not just より, the meaning is clearly "by/with/according to" and not "instead of". In the third line, チャンスを与えられた is modifying デュエリスト (and in the context of the show, "duelist" is not a single person, but a term used for all the characters who, uh, fight in the duels). In the last two lines, the fact that it's 決闘勝ち 手に入れる and not 決闘勝ち(を)手に入れる suggests that, rather than the victory of the duel being obtained, victory in the duel leads to obtaining something else, i.e. the Rose Bride.

さあ 私とエンゲージして
参りましょう 天空の幻の城
世界を革命する力 私とともにいる人のもの

Current translation:

Come now, engage me
Let's go, ethereous illusionary castles
The power to revolutionize the world is with the people who live with me

My translation:

Yes, become engaged to me and we'll go
To the illusory castle in the sky
The power to revolutionize the world belongs to the one who is with me

Why it's wrong:

"Engage [someone]" can't really be used in the sense of "make [someone] your fiancée" in any form of English that I know of. Unfortunately there's no really good active verb to use here (again, that I know of), hence "become engaged to me". In the second line, it makes sense to me to assume that the first and second parts of the line are related and they are thus going to the illusory castle in the sky (of which there is only one). The third line is not technically wrong grammatically speaking, but in the context of the show, power belongs to the one person who currently "owns" the Rose Bride, not to multiple people at one time.

Full re-translation:

If it does not break the egg's shell, the chick will die without being born
We are the chick; the world is the egg
If we do not break the world's shell, we will die without being born
Destroy the world's shell!

To revolutionize the world! To revolutionize the world!

We who have been chosen by the Rose Seal
We who gather in accordance with the letters from End of the World
Each of us duelists, given a chance
The victor of the duel will obtain her:
The Rose Bride

Yes, become engaged to me and we'll go
To the illusory castle in the sky
The power to revolutionize the world belongs to the one who is with me

Now, I spend each day
Entirely devoted to Saionji-sama
That is the law of the Rose Seal, the fate of the Rose Bride

We who have been chosen by the Rose Seal
We who gather in accordance with the letters from End of the World
Each of us duelists, given a chance
The victor of the duel will obtain her:
The Rose Bride

To revolutionize the world! To revolutionize the world!