Just Riffing To open a Nephalem Rift you need 5 Rift Keystone Fragment's that can be obtained in by completing adventure mode bounties. Adventure mode is unlocked by completing act V in the story. To open the portal you use your 5 Fragments on any Nephalem Obelisk which are located in any town.
Killing enemies by your hero's hand you will gain progress toward this achievement. It is cumulative, so you do not need to do it all in 1 rift.
Good luck and have fun.