Do the theme dungeon quests. They are designed to give good experience for your level. For example, the Ellinel Fairy Academy dungeon has quests that can quickly boost your level.
You can level up fast by completing all the assigned tasks and challenges. Also, interacting frequently with other characters and joining clubs can help.
Complete missions with a high difficulty level. These often give more XP. You can team up with friends who are also good at the game to increase your chances of success. For example, some heist missions in online mode are not only challenging but also rewarding in terms of XP when completed successfully.
I'm not aware of any legitimate cheats to level up fast in High School Story. The game is designed to be played over time, and leveling up should be based on your in - game achievements and progress. Just keep playing, participate in events, and complete tasks.
Do a lot of missions. The story missions usually give a good amount of XP. Also, participate in races. Even if you don't win, you still get some XP for taking part.
One way is to complete quests regularly. The more quests you do, especially the ones with higher difficulty levels, the more experience points you'll get. Also, try to battle stronger monsters as they give more exp when defeated.