Coming from Perth, Western Australia, Greville emerged onto the scene in 1995, winning the 200-metre freestyle at the Australian Championships and going on to win a silver medal in the 4×200-metre freestyle relay at the 1995 Pan Pacific Championships in Atlanta, Georgia.

At the Atlanta Olympics the following year, Greville reached the final of the 200-metre freestyle, as well as collecting a bronze medal in the 4×200-metre freestyle relay, alongside Susie O'Neill, Nicole Stevenson and Emma Johnson.

[1] Greville's emergence was complete when she claimed a bronze medal in the 200-metre freestyle at the 1998 FINA World Championships in Perth, as well as the relay event.

[2] Due to this injury, Greville withdrew from the 1999 Pan Pacific Games in order to surgically repair her shoulder.

Greville swam trials with an injured shoulder missing selection for the 2000 Summer Olympics.