This is a fairly easy trophy you will gain through just playing the game, as staggering happens a LOT and it's an extremely useful thing to do in the game, I'm not sure of the /exact/ number, but it's not too big nor is it too small, i.e 10-20.
In order to stagger an enemy, you have to fill up their chain gauge in battle, which is the yellow bar in the top right, it will go down as you do not attack so try to keep your attacks up on the enemy if possible, the classes that are the best and main ones for fulfilling chain gauges are Ravagers, but it'll run out quickly if a commander does not attack. What I do is attack with a Comm then switch to Ravager duo/trio and fill it up asap. Do this as many times as you can and it'll be yours.A note for another easy way to fill up chain gauges and gain another trophy doing so;
Before you get into a battle, and you see the enemy running around, run up to the enemy and press
so your character does an attack animation, if done successfully it'll say "Great" and initiate battle, this will cause a "preemptive strike", which will let your chars automatically hit first and filling up the enemies gauges halfway on attack which is very helpful for chain gauge filling, and if done a certain amount of times will reward you with the following;