In 2013, Rodriguez had her breakthrough season, she won the 2013 Mediterranean Games in Mersin beating Greek gymnast Varvara Filiou (silver) and France's Kseniya Moustafaeva (bronze).

[1] at a press conference, Rodriguez announce her plans to continue competing until the 2016 Olympic Games in Rio de Janeiro, Brazil.

In July, Rodriguez won the all-around gold at the Izmir International Tournament ahead of Jana Berezko-Marggrander.

On 9–13 September, Rodriguez competed at the 2015 World Championships in Stuttgart and finished 9th in the All-around finals with a total of 70.248 points.

[2] On 12–13 March, Rodriguez competed at the MTM Tournament in Ljubljana, Slovenia finishing 4th in the all-around with a total of 70.750 points,[3] in the apparatus finals; she won a silver in ball.

On 1–3 July, Ashirbayeva competed at the 2016 Berlin World Cup finishing 8th in the all-around with a total of 70.250 points and qualified to all 4 apparatus finals.