The impeachment process is strictly following the Constitution and being closely monitored by the Supreme Court. The majority of the Brazilian population, the majority of deputies and the majority of senators support it. The majority of foreign watchers consider it a legitimate process. It is not a coup by any stretch of the imagination.
A valid impeachment needs to follow from legitimate charges of wrongdoing according to the constitution. The charges against the president have not been ruled as crimes, unlike what happened for example to Mr. Collor de Mello in the 90s. The charges are merely accusations, which need to be proved beyond doubt. Therefore, the whole process is illegal. The congress and the majority of the country are betting on the fact that the charges will be considered as real crimes by the supreme court, but there is a lot of questions if this will eventually happen (contrary to what the media is promoting). The government, on the other hand, is pretty sure that there is no crime involved. Because of the shaky ground of the whole process, a large number of jurists consider the whole thing to be a coup.
