After 11 days of competition, Women Grandmaster (WGM) Phung finished third in the women's blitz chess event with seven points from nine matches.
Phung struggled with one loss and two draws in the first three matches. But she came back strongly with six wins in a row and grabbed her bronze medal.
WGM Divya Deshmukh and WGM Gomes Mary Ann, both of the hosts, ranked first and second, respectively.
In the standard event, Phung came in fourth position with 6.5 points.
The top three were all from India - WGM Pallathur Venkatachalam Nandhidhaa, WGM Priyanka Nutakki and Deshmukh.
The championship saw 140 players from 13 countries. Vietnam sent three female competitors - Nguyen Thanh Thuy Tien, Nguyen Thi Mai Hung and Phung - and one male player, Dang Vu Dung.
Tien, Hung and Dung did not reach their best performance in this competition, ranking out of the top five in all two categories.