¡Hola, Rosa!
Una vez más he traducido la misma canción que tu, pero es una de mis favoritas. Lo siento.

As for your translation I like it and I think that the tile you used “Trying to conquer you once again” is fantastic. I love the word “conquer” that you have chosen. It suites here absolutely perfect (thefreedictionary.com definition: to gain the love, sympathy, etc., of (someone) by seduction or force of personality) and I don’t think that any other choice would have been better.
For me “conquer” has also some connection with Spanish “conquistar” and “conquistador” - “se aplica a la persona que consigue el amor de otra persona con facilidad” but also “se aplica a la persona o ejército que consigue el dominio y control de una población o de un territorio como consecuencia de una guerra”, so the meaning of these words both in Spanish and in English is the same.
I would suggest you to leave this title as the only one and write the other one in comments.

Stanza 6, verse 4: I think it would be safer to use “that” instead of “it”.

Stanza 7: I know that you can “give promises” or simply “promise”, but I don’t think you can “swear promises”, because it’s something that we call in Poland “buttery butter” - “to swear” means in fact “to promise” (dictionary.cambridge.org definition: “swear - to promise or say firmly that you are telling the truth or that you will do something or behave in a particular way”).

Last stanza: “seeing the stars with you” sounds strange. I think it should be rather “looking at the stars”, as you wrote in comments.

Anyway, I think you deserve the five stars that I gave you.

Mucias gracias.