Fishing is best during the first part of the dry season (April to May), when the flooded rivers settle back into their channels, but locals have been known to lasso 80kg fish throughout the dry season. This is some of the best fishing in the world. There are three species of piranha, as well as the tasty dourado (known locally as the river tiger) that reaches upwards of 9kg. Other excellent catches include pacu, suribim, bagre, piraputanga, piapara, cachara, pirancajuva and pintado, to name but a few.
Fishing – with the required permits – is encouraged between March and October. It is, however, prohibited during the piracema (breeding season) running roughly from November to February.
The Brazilian government issues recreational fishing licenses (licença de pesca amadora), but you'll need to negotiate the website in Portuguese: http://pndpa.mdic.gov.br/pndpa/web/pesca_amadora.php.
To fish from a boat, you will need the embarcada license (R$60; the shorebound desembarcada license is R$20). It lasts for a year and is free for seniors. You'll need to use a Brazilian address. Print off the temporary form, take it to any bank or lottery seller to make the payment, then print off the permanent license once it is issued.