Kuzmina ya wakilci Slovakia daga Disamba 2008 kuma ya lashe lambar azurfa watanni biyu daga baya a farkon farawa a gasar Olympics ta duniya.
Gasar Cin Kofin Duniya ta Biathlon ta 2009 a Pyeongchang. Ta lashe lambar zinare a tseren tseren kilomita 7.5 da lambar azurfa a tseren kilomita 10 a wasannin Olympics na hunturu na 2010 a Vancouver, British Columbia, Kanada. Nasarar Kuzmina ta sanya ta ta biyu Slovak bayan Ondrej Nepela don lashe lambar zinare ta Olympics ta hunturu, kuma ta farko ga Slovakia mai zaman kanta. Ta kuma lashe lambar yabo ta tagulla, a Gasar Cin Kofin Duniya ta Biathlon ta 2011 a Khanty-Mansiysk. A Wasannin Olympics na hunturu na 2014, ta sake lashe lambar zinare a tseren kilomita 7.5. A wasannin Olympics na hunturu na 2018, ta dauki lambar yabo ta azurfa a cikin bin da mutum kafin ta dauki zinare a cikin farawar taro, ta buga 19 daga cikin 20 don zama dan wasan biathlete na farko da ya lashe lambar yabo ta zinare a wasanni uku a jere, kuma ya ɗaure ta a matsayin 'yan wasan Slovak da ke da mafi yawan zinare na Olympics tare da' yan wasan canoe Pavol da Peter Hochschorner.