This is the longest trophy in the game. Each character are maxed at level 20 and you gain XP after each fight playing with that character. After doing all other trophies you may have 1 or 2 characters around level 20, so you need to grind the rest.
There are a few methods to boost it, but it depends if you have or not a second controller. Make sure you move the settings selecting only one round per match playing versus.
Select your desire character and play against your second controller or AI on Very Easy. Make your way to beat him as fast as you can, you can rematch as many time as you want. Each fight will grant you around 250-400 XP but it depends if you made a Perfect Victory, try to don’t use any supermove, it gives you more XP but it takes way long to perform.
Doing this you can finish a fight in 30 seconds, and to reach level 20 you need around 4,900 XP (from level 19), so doing some math you can max a character in 2-3 hours, give or take, and maximize all 28 characters could take you 60-80 hours of full dedication.
Also there is an alternate way to maximize all characters faster but it costs real money, around $100 USD, so if you prefer to buy some Source Crystals in the Store you can get this trophy in a really shortest time. Make sure you reach your last level 20 character by your own.
Another great method to maximize your characters is by using a turbo controller in the Battle Simulator, here you can maximize three different characters at the same time, leaving the game over night while your three characters level up automatically pressing Cross while your sleep.
Finally another XP farm method. This one seems the most efficient way to level up faster, but you need two controllers:
Change the Fight Time to 300 and 2 rounds (from Options at Main Menu), and turn off the level handicap in the Match Options (both players press Square before selecting the map). Doing this will make your AFK rival be at level 1 all the time and he will receive the most damage in-fight.
Once the fight starts make your way to finish the match as fast as you can, if you can beat your AFK rival around 280 left in the clock with two Perfects you can earn like 1,050 XP in 30-35 seconds. If you play another 60 fights you will be maximizing your fighter in less than 40 minutes!.
Using this method you should be able to pop this trophy in around 20 hours, give or take.
Here is the video for a full reference: