The fastest way to master a certain Support Talent is by keeping it equipped at all times until it's maxed.
The first Support Talent you are most likely to master (if equipped and if you're exploring most parts of each map and finding discovery points and monoliths) is Sorey's Point of Interest Detection.
The easiest Support Talent to master is Edna's Money Finding; it just requires you to move around to level it up, which you are doing at all times anyway.
You can view the level of all your characters Support Talents by pressing the 'Options' button and selecting the 'Support Talents' menu option.
You need to get the Support Talent to level 20 and then continue to level it through 20 until it says 'MAX' above the progress bar, at which point the trophy will unlock.