Orellana’s account is a good suggestion. My guess is that tuberculosis and syphilis were the most deadly because of their long incubation periods. They would spread far and wide before people found out how sick they were.
From my readings, syphilis was brought to Europe by the explorers returning from America. I believe some called it the French disease. I suspect that the more common diseases like smallpox, measles and others did the most killing. I don’t know how quickly Orellana and crew arrived on the Amazon. Once there and exchanging germs, river traffic by the residents would have spread infections quickly up and down the Amazon and into tributaries.