Here is the completed text using the present perfect form of the verbs:
Yevgeniya Kanayeva is the only rhythmic gymnast to win two Olympic all-around gold medals, winning at the 2008 and 2012 Olympics. She began gymnastics at the age of six. Year by year, Zhenya (1) has shown her desire to try out new elements and adopt new styles. She (2) has competed in Baku, Beijing, Montpellier and London. She (3) has participated in lots of international competitions in other cities too. She (4) has won 13 gold medals in the European Championships. She is the first gymnast who (5) has earned gold medals in all of the apparatus (rope, hoop, ball, clubs and ribbon).