This can be done in any game mode. For me the easiest was in Survival as there is no requirement for what you must score and you can end it by simply letting the 'boss' predator (bear or whatever big animal is featured in the level you choose) kill you at the end of the cycle. I tried to count out 15 shots as there was an achievement that required 15 legal kills in a level, I have no idea if they are related or if it is required... I'll have to test with another profile. Make all your shots count. There aren't any grenades to up your accuracy.
Access Survival mode by choosing Play Game from the Main Menu, then Galleries. From here you can cycle through the hunts until you find one that says Type: Survival above the map.