The phrase is old-fashioned and rarely used in modern conversation or writing. Reading Shakespeare, I noticed characters often vowed to 'be revenged on' their foes.
Pro Tip 2/3
Vengeful Context
It's used in situations involving deep anger or desire for retaliation, not mild annoyance. After the relentless bullying, he muttered he would 'be revenged on' the culprits.
Pro Tip 3/3
Personal Wrong
The phrase implies a response to a personal grievance or injury. When her brother was wronged, she pledged to 'be revenged on' the slanderer.