Successfully complete the game to unlock New Game+ mode, the Let's Go Arche mini-game, additional music in the Sound Mode menu, and an alternate title screen color.
Go to Ymir Forest, then run around and fight people to get lots of experience. When you are low on health, get Arche, exit, come back, and leave Arche. You will be completely healed. Repeat this until reaching the desired level. Note: Arche will not level up with you.