Make no mistake: Balthazar is bad to the bone.
But he's not much of a schemer from what we can tell. Yes, he commits the first murder of the play (and we only get a report about this). And yes, that murder is the first domino to fall in a series of tragic deaths. Still, he doesn't really do anything interesting for the rest of the drama.
In fact, the only thing we really see him do is creep on Bel-Imperia. He certainly goes along with all of Lorenzo's murder business, but he doesn't exactly aid and abet. Instead, he just obsessively pursues Bel-Imperia while everybody else does all the dirty work. So, maybe it's best to think of him as a lazy aristocrat completely lacking moral scruples. And how.
Other than that, he's a really flat character. Still, his weird indifference to human life and mistreatment of Bel-Imperia are more than enough to make him a powerful object for revenge. In fact, this kind of bad poetry also makes him a great target for revenge:
Yet might she love me to content her sire;
Ay but her reason masters his desire.
Yet might she love me as her brother's friend;
Ay, but her hopes aim at some other end.
Yet might she love me to uprear her state;
Ay, but perhaps she hopes some nobler mate. (2.1.21-26)
Real talk: this poetry stinks. Making it likely that Kyd made him a bad poet on purpose, just so we could hate him even more.
His snobbery also comes through at the end when he proposes that she might love him just to "uprear her state" (or become more important). Since he can only imagine losing out to some "nobler mate," we learn that he doesn't really get love at all, which explains the bad love poetry. Oh boy, just wait till he finds out that she digs the down home boys.
In the end, he's the kind of bad guy we love to watch die. And in that respect, he dies well.