Most of south america broke away from colonial powers between?

between 1810-1850.

Explanation: this is so-called first cycle of decolonization in the world. Majority of south-American countries took advantage for that step in Napoleonian context. Inspired by the events of the French revolution and progressive ideas of French Enlightenment, local population started calling for independence and (in the case of Hispanic part of that continent) for republican form of government. British Guyana and Dutch Guyana got independent in the 2nd part of the 20th century. French Guayana continues being French. Last attempt to conquer south American territory was made by Spaniards (Peru) in 1860s.