Kill the normal mobs that spawns and after you defeat a wave of them, the Manticore will fly in and engage you. During this time, do not attempt to attack it. Instead, simply stand on that glowing tiled area and wait for the Manticore's barbed tail to strike down at you. You can dodge out of the way and if you time your dodge before the striking animation as well.
Rinse and repeat this 3 times and you will eventually start the focus kill button press chain.