되다 = meaning of "become"
되 = root of 되다.
고 = end of word
싶다 = meaning of "hope or want"
싶어요 = honorific form of 싶다.
For example, If you want to say, "I want to go"
1. go = 가다 but 가다 is a root so you should change it in a sentence to "가고"
2. want = ~~싶다. if you want to change it as a honorific form, it should be "싶어요"
so complete sentence should be " 가고 싶어요" (not honorfic form is "가고 싶다")
you can drop "I" but if you use "I" --> "나는 가고 싶어요"
But "나는 아름다운되고 싶어요" is wrong in grammer.
If you want to say "I want to be beautiful" --> "나는 아름다워지고 싶어요"
becuase "아름다운" is adjective so can't use with "싶어요" together.
Always, ~~싶어요 should be used with verb.
for example, 가다(verb:go) + 싶다 = 가고 싶다. 먹다(verb:eat) + 싶다 = 먹고 싶다.
So you should change from adjective form to verb form.
아름다운(adjective)-->아름다워지다(verb: become beautiful)
I hope this will helpful to you.