You'll need to continue the story until you have at unlocked all 5 devour modes, as three of them will be locked at first.
Prior to a battle, you will need to assign a different effect to each of your Predator Styles, which is in your Loadout menu. It's recommended that have Burst Savour in this list, to provide yourself a larger window to pull off all the required techniques.
As for your Party, bringing at least 1 "New-type" God Eater, such as Alisa or another player as they can shoot one of their Burst bullet to you to extend your burst. Alisa will regularly send you a Burst Bullet. (Most Storyline characters are "Old-Types" so Soma and Kota can not do this, however they can help in the actual fight.) However with enough practice and skill a player can do this trophy solo, with no other players or NPCs helping.
A Quadriga Type Foe is recommended, as its slow, tall and can take alot of Punishment.
As for the Devour Types (Default PS4 controls) :
Charge Devour - Hold Triangle
Quick Devour - R1 + Triangle
Combo Devour - Square or then R1+Triangle (Quick Devour after a successful attack)
Step Devour - Move+Circle then R1+ Triangle (Quick Devour after a "dodge")
Air Devour - X then R1+Triangle (Quick Devour in the air.)
The Trophy will pop on Mission completion.