After deciding to turn her life around, Giglia researched several sports to join and attended a para-cycling selection camp for women. A year on from her stroke she was classified as a C3 athlete and was accepted on to the British Cycling Paralympic Development Programme.[3] Over the next six months she progressed through the Great Britain talent scheme until she progressed to the Academy in October 2014.[4]
Giglia was selected for the Great Britain team at the 2015 UCI Para-cycling Track World Championships in Apeldoorn. She finished just outside the medal positions in both the C3 500m time-trial (4th) and the C3 individual pursuit (4th).[5] She was then selected for the 2015 UCI Para-cycling Road World Championships in Nottwil in Switzerland; but again failed to medal with two fourth places in the time trial and the road race.[5] The year ended with a major break-through for Giglia when she beat the reigning world champion, Denise Schindler, in the C3 individual pursuit.[5]
In 2016, in the buildup to the Summer Paralympics in Rio, Giglia entered her second World Championships. There, at Montichiari in Italy, she won gold in both the C3 500m time-trial and the individual pursuit setting new world records in both events.[5]
On the first day of the 2016 Rio Paralympics, Giglia won the women's 3000 m individual pursuit (C3), Great Britain's first medal of the Games.[6]
Giglia was appointed Member of the Order of the British Empire (MBE) in the 2017 New Year Honours for services to cycling.[7]