Start a Private Beast lobby - you can do this alone, or with friends which will make it easier - and simply complete waves 1 to 12 on the Fenix Rising DLC maps, which are:
Academy
Anvil
Depths
Escalation
The Slab
There is a counter in the Stats and Awards - Achievements tab which will tell you how many waves on each map you have completed.
It is also possible to get this in Public Beast matches but since there is no guarantee what maps will be selected for the vote, you may be trying a while before you've gotten all five.