On Wikipedia, I came across a page (in PT) showcasing the bairros (neighborhoods) of Belém and as an added benefit, it broke them down by zones (not sure what to call them, perhaps municipalities). I’ve heard all but the first zone used in daily conversation as the bairros that make up the Zona Central are just referred to by their name.

Zona Central

Batista Campos | Campina | Cidade Velha | Nazaré | Reduto | São Brás | Umarizal | Marco

Águas Lindas | Aurá | Castanheira | Curió-Utinga | Guanabara | Mangueirão | Marambaia | Souza | Val-de-Cans | Universitário

Canudos | Condor | Cremação | Guamá | Jurunas | Terra Firme

Águas Negras | Agulha | Campina de Icoaraci | Cruzeiro | Maracacueira | Paracuri | Parque Guajará | Ponta Grossa | Tenoné

Aeroporto | Ariramba | Baía do Sol | Bonfim | Carananduba | Caruará | Chapéu Virado | Farol | Mangueiras | Maracajá | Marahú | Murubira | Natal do Murubira | Paraíso | Porto Arthur | Praia Grande | São Francisco | Sucurijuquara | Vila

Água Boa | Brasília | Itaiteua | São João do Outeiro

Benguí | Cabanagem | Coqueiro | Parque Verde | Pratinha | São Clemente | Tapanã | Una

Barreiro | Fátima | Maracangalha Miramar | Pedreira | Sacramenta | Telegráfo

As a bonus, each bairro page gives a tiny history of each bairro as well as principal streets to be found there and the linhas de ônibus (bus lines) that pass through there (a fact which I will add to the bus post I recently did).