Desgraciado literally translates to "unfortunate" or "disgraced", but in common usage, especially in a song like this, it's a strong insult meaning "wretch," "scoundrel," or "bastard."
In "Amiga Date Cuenta," the word is used to describe the cheating boyfriend, emphasizing the friends' disdain and anger towards him. It's a powerful and emotionally charged term that perfectly captures the song's theme of female solidarity against a deceitful partner.
This is one friend telling another the truth she doesn't want to hear. Ha*Ash and Thalía spend the first verse laying out the pattern: "Entre falda y falda, él te ha ido mintiendo como miente un niño" [Between skirt and skirt, he's been lying to you like a child] — a guy who's outgrown being a kid but hasn't outgrown lying like one. The chorus doesn't bother being gentle about it: "Si él no merece tu amor... ya no dudes en dejarlo" [If he doesn't deserve your love... don't hesitate to leave him].
What keeps it from turning into a lecture is what comes right after the advice. "Aquí me tienes a tu lado" [Here I am by your side] isn't a slogan, it's an offer — she's already lived through the same thing ("Yo ya estuve en tus zapatos amarrada a un mal amor" [I've already been in your shoes tied to a bad love]), so she knows exactly what a whole night spent forgetting him looks like, and she's showing up for it. The title says the rest: amiga, date cuenta — friend, wake up.