Como dizer "Trabalho de formiguinha" em inglês

Eu diria "thorough work", ou seja, "trabalho meticuloso". Nem todas as expressões populares se traduzem para outros idiomas, então temos que focar na ideia geral.

My two cents.
Could also be: "we work together, in a multidisciplinary. To provide comprehensive health care for you/to address the patient's needs. Since we acknowledge that that is a work involving people, emotions, and [1] expertise.

[1] I got tempted to use "professional expertise" but expertise is by definition professional, perhaps they would use that form anyway. Or they could opt for "medical and scientific knowledge.".

Ah! More advanced learners might make it shorter or improve it somehow.

Somehow the 'ants work' here would be in the sense of (multidisciplinary) teamwork, not perseverance or other aspects. Also, in the coordination/complementarity side.

No exact translation, but I think the idiom "It takes a village" expresses the same idea, where a team must work together as if they were a very close community or colony in order to accomplish something.

See the examples in this article: grammarist

Ref. idioms.thefreedictionary

That's also a very good example Bryan, in a certain context. You rock!