At the 6th Doha FIG World Challenge Cup in Doha, Qatar, on 28 March 2013, Phan placed first in the vault final, ahead of Romania's Larisa Iordache and Switzerland's Giulia Steingruber, with an average score of 14.825. She went on to compete at the 2013 World Artistic Gymnastics Championships in Antwerp, Belgium, and qualified to the individual vault final. In the final, she attempted a more difficult vault, the Amanar, but fell and finished seventh. Phan began 2014 by winning a World Cup title on the balance beam in Osijek. At the 2014 Asian Games in Incheon, South Korea, she qualified to three event finals: vault, balance beam and floor exercise. She finished third on vault, behind Oksana Chusovitina of Uzbekistan and Hong Un-Jong of North Korea, the reigning world champion; second on balance beam, behind Kim Un-Hyang of North Korea; and eighth on floor exercise. Two weeks later, she competed at the 2014 World Artistic Gymnastics Championships in Nanning, China. She qualified for the vault final but finished eighth with major errors. In the spring of 2015, she won the balance beam titles at two World Cup events. Under pressure to medal in the team event at the Southeast Asian Games in Singapore, she led a minimal team of four gymnasts with Đỗ Thị Vân Anh, Đỗ Thị Thu Huyen and newcomer Long Thị Ngọc Huỳnh. The team was plagued with injuries and finished fourth, but Phan qualified for all of the individual events. She went on to win the most gold medals of any gymnast at the competition, as well as a bronze on floor exercise. At the 2015 World Artistic Gymnastics Championships in Glasgow, she finished 85th in the all-around in qualifications with a total score of 51.033: 14.400 on vault, 10.233 on uneven bars, 13.300 on balance beam and 13.100 on floor exercise. Because of injuries, she opted not to attempt a second vault to qualify for the vault final. Phan finished 41st in the all-around competition at the 2016 Olympic Test Event to qualify for the 2016 Olympic Games in Rio de Janeiro. Competing with an injury, she scored 14.300 on vault, 11.600 on uneven bars, 13.800 on balance beam and 13.000 on floor exercise. One month later, she competed on vault and balance beam at the World Challenge Cup in Varna and finished second on both events. At the 2016 Olympics, Phan competed on two events in the qualification round: vault and balance beam. For her first vault, she performed a double-twisting Yurchenko and scored 14.700. Her second vault, a handspring pike front with a half twist, was much less difficult and scored 13.766. With an average score of 14.233, Phan was 17th out of 19 competitors who performed two vaults. On the balance beam, she scored 13.800 and finished 36th out of 82 competitors.
