Murphy competed at the 2012 Summer Olympics in the Women's Laser Radial class. She won her first four days of sailing at the London Olympics and, on the fifth day, came in 8th and 19th position. On the sixth day of sailing she came 2nd and 10th and slipped down to second, just one point behind the Belgian world number one. She was a very strong contender for the gold medal but in the medal race she was overtaken on the final leg by her competitors and finished in 4th, her personal best at a world class regatta.
Murphy won her first major medal at an international event when she won gold at the 2013 European Sailing Championship. She was nominated for the 2013 RTÉ Sports Person of the Year in December 2013.
On 16 August 2016, Murphy won the silver medal in the Laser Radial at the 2016 Summer Olympics. In December 2016, she was honored as the Irish Times/Sport Ireland 2016 Sportswoman of the Year.
2016: Summer Olympics, Rio de Janeiro, Brazil – Silver
2013: European Championships, Dublin, Ireland – Gold
2012: Summer Olympics, London, UK – 4th
2011: World Championships, Perth, Australia – 6th
2010: Skandia Sail for Gold regatta – 10th
2010: Became the first woman to win the Irish National Championships.
2009: World Championships – 8th
On 11 August 2012, Murphy was a guest on Saturday Night with Miriam. On 15 May 2013, she was a guest on The Ray D'Arcy Show on Today FM, and was interviewed by Alan Hughes on TV3's Ireland AM. She appeared on The Late Late Show on 2 September 2016.