In the mixed 4x100 m freestyle relay, Vien and her brother Nguyen Quang Thuan along with teammates Tran Hung Nguyen and Nguyen Thi Bich Ngoc set a new record with a time of 3 minutes, 38.88 seconds.
The team went on to break the 4x200 m freestyle relay record with a time of 7 minutes and 48.63 seconds.
Vien broke two more records, this time in individual events, clocking 2 minutes and 11.3 seconds in the 200 m freestyle and 4 minutes and 13.81 seconds in the 400 m freestyle.
In the competition that concluded on Monday, the 24-year-old won 17 golds and three silvers.
She almost made a clean sweep of the individual events she competed in, losing only the 50 m freestyle, and by a mere 0.01 seconds, to Pham Thi Van.
Her team Quan Doi topped the medals tally with 22 gold, 11 silver and seven bronze medals. In second place was HCMC with seven golds, nine silvers and six bronzes.
The swimmers will now prepare for the national age group championship to be held from May 19 to 21. The event will be used for Olympic qualification.
Nguyen Huy Hoang is the only Vietnamese swimmer to qualify so far. He will compete in the 800 m freestyle and 1,500 m freestyle.