You need to build up the meter at the bottom of the screen. I think you need to kill 1000 mobs for it to be full. Apocalypse form is quite useless, other than it making you invulnerable. In my human form I do around 3x more damage. I never use it, only when trying to learn a boss' skill rotation. Next to this, it is difficult to learn the Apocalypse form skills and their potency, as you only get like 30 seconds of time to test them and it takes 15-20 minutes to get enough kills to try again for 30 seconds.

You have to press F first to open up the tab for Apocalyptic forms and then select one of your choice. Your primordial essence doesn't have to be at max capacity to use it, you can use it whenever but of course using it when you have max primordial essence will make it last longer.

There's apocalyptic shrines on the open world map that refill your bar