Pechando comes from the verb pechar, which literally means "to butt with the chest" or "to push with the chest." In a more colloquial sense, especially in some Latin American regions, it means to insist, to push for something, or to confront.
In the song, the lyric "sigue pechando que se acabó todo" implies that the ex-girlfriend keeps insisting or pushing the narrative that everything is over, even though her actions suggest otherwise. It's an interesting word choice that adds a layer of stubbornness and denial to her character.
Get ready for some classic Vallenato drama with Peter Manjarrés' "Que Belleza"! This song is all about a guy who's definitely not over his ex, and he's got some strong opinions about her post-breakup behavior. He starts by saying, "Ay qué belleza / Como fui yo quien la terminó vive hablando locura" [Oh, how beautiful / Since I was the one who ended it, she lives talking crazy]. He claims she's out in the streets badmouthing him, saying their time together was