There is a number of ways that Portugal and other European nations tried to challenge Spanish power:
1. illegal trade with Spanish colonies - given that Spain forbade any nation to trade with their colonies in the Americas, they had to do it illegally, without Spanish knowledge. Smugglers had a special role in this given that they did most of the work
2. pirates - these nations tried to do everything in their power to diminish the authority Spain had in the Americas. This is why they resorted to privateers - that is just a fancy name for pirates who preyed on Spanish ships in order to steal their treasure
Spain was incredibly strict when it came to trade and what came into their nation, so the Portuguese found a way around that and would smuggle in illegal contraband all the time. They used that, force, and discipline to further divide the Spanish.
