Glims are the orbs enemy leave behind during battle, they are green, blue and gold.
Glims drop when you get a "nice" or when you counter an enemy.
The trophy is fairly straightfoward BUT the only glims that count are the ones collected by the character/familiar you are controlling during battle.
Also, as far as I can tell, the glims collected at the end of the battle, through the upgrade bought with merit awards DON'T count for the trophy.