I wasn't aware of João Gilberto (partially because its musical genre, "Bossa Nova", doesn't really fit my personal tastes). Some of his songs (such as "Lobo Bobo", which is Portuguese for "Fool Wolf" and plays some pun with the story of Big Bad Wolf) do indeed contain rhythm and regular metrics.
As for the phrase you mentioned, "Para machucar meu coração", it depends heavily on the surrounding context. For example, "Você fez de tudo / para machucar meu coração" would translate to "You did everything / to hurt my heart", while "Para machucar meu coração / Bastou não pedir perdão" would roughly translate to "In order to hurt my heart / not asking for forgiveness was enough" (the latter example contains the rhyme "coração/perdão" which was lost during translation). Plus, there are several ways to translate the same text/sentence as well: "You've gone too far / hurting my heart" would be a valid translation alternative to the first example (although it would slightly change the verb tense from the original).
There's also the Portuguese interchangeability of subject and predicate, verb and adjective, etc, the "word order" (which for English is often SVO, Subject+Verb+Object). Something like "No meio do caminho havia uma pedra, havia uma pedra no meio do caminho" (a famous quote from Carlos Drummond de Andrade) has a direct English translation "In the middle of the road there was a stone, there was a stone in the middle of the road" which sounds okayish for an English-speaker, but literally translating phrases such as (I just invented this one) "Caminhava pela ponte o senhor do meu destino" to "Walking across the bridge (was) the lord of my fate" probably sounds "weirder" than the non-literal translation "The lord of my fate walked across the bridge".
It's worth mentioning that there are some English things that Portuguese cannot translate, either. For example, "hopefully" is a word that I can't really find a proper Portuguese synonym ("Esperançosamente" sounds too weird). "Enshittification" is another example: a neologism that often gets "enportugueseficated" as "enshitificação". Some phrases specific to the English language also tend to have no direct translation (e.g. "Every cloud has a silver lining" seems to be a frequently-used English idiom which has no direct Portuguese idiom, and its literal translation "Toda nuvem tem um forro de prata" is not really meaningful to a Brazilian context).
Finally, there are things that neither language can really convey, a phenomenon I mentioned in my post entitled "Ineloquibilis" from January. Things like "non-existence" and "lack of spatial characteristics" are hard to be put into words, be it English or Portuguese, because language implies "time" (hence the presence of tenses for verbs) and "existence" (hence the verb "to be"). So a sentence such as "The eldritch entity, full of devoid non-beingness, shone its darkness unto me, from forever till the neverness, its non-existence is awesome and ominous" sounds really weird and implies something ("Eldritch entity") being not-a-thing (thus not existing), yet the original meaning is something that "exists in the non-existence", a paradoxical statement... and it's only paradoxical because of the intrinsic nature of human language. Portuguese doesn't help here, either: "A entidade sobrenatural, cheia da vazia inexistência, iluminou sua escuridão sobre mim, desde sempre até o nunca, sua inexistência é maravilhosa e ameaçadora" also sounds weird.