General:
* Victory
* Domination
* Subjugation
* Overthrow
* Capture
* Acquisition
* Takeover
* Seizure
* Occupation
More specific:
* Annexation (for taking territory)
* Suppression (for overcoming resistance)
* Overcoming (for achieving victory)
* Claim (for taking possession of something)
* Subdue (for bringing under control)
* Vanquish (for defeating in battle)
Figurative:
* Master (for gaining control over something)
* Win (for achieving something after effort)
* Breakthrough (for overcoming a difficult obstacle)
The best synonym to use will depend on the specific situation and the nuance you want to convey.