Like a lot of games, you will gain experience as you defeat enemies and complete quests. Once you have accrued enough experience, you will level up and get stronger. The max level in the game is level 50, which is what you need to reach with any character, in order to unlock this trophy/achievement. You will probably finish the main story around level 35 or so, depending on how much exploring you do, which means you will need to grind out the rest of the levels.
Upon completing the main story, you will unlock Hard difficulty, and you can change the difficulties at your base in the Residential District. Hard difficulty will basically increase the levels of enemies, making it so they are slightly more difficult to defeat, but they give more experience. The best thing to do is craft the accessories that give more experience, get the EXP buff from the Inn, then go to one of the late-game areas like the Runebarrows or Lava Ruins, then run through those while killing all of the enemies. Remember that resting at your base will reset the Inn buff, so if you need to heal, do so with the Tavern’s food.