As you may know, 1.6 added two new monsters to the game for players who have the DLC. (Note that the DLC is required to encounter these monsters.) The question comes, of course, how to get them, and here's how:
* At some point, you will get a mission that mentions the new monster type. Clearing it will unlock a hunt, on one of the spots that normally has a large battle.
* The hunt will have you fighting a tier 3 boss of that type, as well as a tier 1 normal enemy. I recommend taking Bzaro and somebody with the Wrangler skillset; this will get you 3 essences from that monster type if you tame the normal enemy. (Note that there's other enemies in the hunt, and Extra and Elite enemies will appear if the difficulty allows them.)
* If you want to catch more of the monster, or you want to get more essences, you can do a large patrol of the map; one of the enemies on the map will be replaced with a tier 2 monster of the new type. This happens only if you've beaten the hunt, but the new monster will always be present. (Note that you do need to beat the large battle here before you can patrol.)

If you catch the monster in the hunt, and you use Bzaro both times, it is possible to get the class for Bzaro doing only 1 large patrol.

(Note that I haven't actually done this myself; I obtained the information about the enemy showing up in a large patrol through data mining.)