How do I get jobs in public health field and NGOs in Brazil

Massively difficult, verging on impossible, without sponsorship and the ability to speak, read, and write Portuguese.   If your current employer has operations in Brazil and would be willing to transfer you, that would be your most viable option.

Thanks a lot for the prompt response. I wonder if there are immersion programs through which one can learn Portuguese in a fast-track manner while exploring job options in the health and development sector.
By the way, I have 2 post-graduate degrees in different aspects of public health, and would considering doing a PhD in a university in Brazil within my area of expertise be of any help, should the universities have a global outlook by allowing some studies in English?

Sorry - no good news, I'm afraid.
The language of instruction in Brazilian universities is Portuguese, as the language of instruction in French universities is French, or German in German universities.
Immersion courses in Brazil are surprisingly difficult to find:  the Brazilian Embassy in Abuja may be able to give you some leads.  And don't forget that there are Portuguese speaking countries in West Africa where you may be able to get a head start.
Unless the country where you earned your degrees has a mutual recognition agreement with Brazil, having your academic credentials revalidated in Brazil requires presenting your diploma, official descriptions of every course taken, tally of classroom hours for each course, and perhaps additional documents, translated into Portuguese by a sworn translator in Brazil, to a public university in Brazil that offers a similar course of study.  A committee of that university will evaluate the material, and decide to accept or reject.  The process seems designed to be difficult and opaque, and succeeds.

As abthree said it's nearly impossible to do what you want to do. Checkout the African nations that speak Portuguese first. Once you master the language, then come here. Or transfer here with a NGO since you have experience with that.

It is very difficult for Expats to find work in Brazil. To be successful you either are independently wealthy, retired, own a business, work remotely from here or teach English (this option is last because it pays very little or you teach privately and work terrible hours). Government jobs are impossible and I doubt you will every get one.

Thank you both for the honest responses. It's really interesting to hear that expats struggle to get jobs, as I'd assumed that the Brazilian economy being the largest in Latin America, that the country will be a very open and welcoming to foreigners. Nigeria has strong cultural links with Brazil dating back to the period of slavery and  post emancipation when some slaves repatriated to Nigeria and settled in Lagos; famous Brazilian quarters! And large percentage of Afro-Brazilians have Yoruba heritage and identify with the the language, culture and traditional religion - Orisha!

I reckon that we do have an appreciable number of Nigerians living in Brazil and from my inquiries, most are into business and not necessarily professionals/expats. So I was curious to know about the potential job opportunities for a mid-career public health professional like me.

The primary reason why I'm scoping for these info is because I have a Brazilian fiancee who's in the early stage of her academic career and can't join me presently in Nigeria, so was exploring possible job prospects in Brazil should I decide to take the plunge and land in Brazil to stay for a few years; maybe via a doctoral program. I did my graduate studies in England and 'm aware that most countries in Europe also run Postgraduate/Research programs in English, including Spain, France, Germany, Sweden, Netherlands, Finland, Norway etc; hence why I asked. In anycase, English is an official language in the EU despite the Brexit plans, but not the same in South America though.

Regarding learning Portuguese I'd be sure to check for alternatives in-country. I do agree that immersion can be possible in the Lusophone countries in West Africa, although Nigerians relate more with the Anglophone and Francophone countries in our region. Portuguese speaking countries are the minority although it's one of the official languages of ECOWAS (Economic Community of West African States), but English and French dominate.

Thanks for all the useful info and advise and I'll keep asking more questions and getting more info...