"进行武装斗争" can be translated into English as "engage in armed struggle" or "carry out armed struggle".
Both expressions are commonly used to convey the idea of waging an armed conflict or resistance. Here are examples in sentences:
The revolutionary forces decided to engage in armed struggle against the oppressive regime.
革命力量决定对压迫政权进行武装斗争。
The group has been carrying out armed struggle for independence for many years.
该组织多年来一直在为独立进行武装斗争。