Overview of how to max a character's level

=General Information=

To max a character's level, you need to do the following 3 things. You need to
 * gain EXP for the character,
 * limit break the character, and
 * evolve the character.

These features will now be described one by one.

Gaining EXP
Gaining EXP is the most basic method to strengten your characters. In general, there are 3 means to gain EXP:
 * The most basic means is to use the character in battle. The amount of EXP gained from doing one quest is determined by the costs you need to pay when you enter the quest.
 * Besides battles, characters can also gain EXP by being sent on a Training Course. Here, the amount of EXP gained is determined by the length of the training course. The merit of doing Training Courses is that this can be done passively, even when you are offline.
 * The third means to gain EXP is to directly feed Enhancement Material to the character via the Upgrade Menu. All 6 elements have 4 different types of Enhancement Material. Good methods to grind these materials are to get them from the Trade Shop or to do the daily grinding quests for Enhancement Material.

Please note that the maximum level that's displayed at first can be increased by doing Limit Breaks on the character or by evolving the character.

Doing Limit Breaks
At the very first, a character's maximum level is rather low. 3* characters can only be raised up to level 30, 4* characters up to level 40 and 5* characters up to level 50. To increase this cap, you need to do Limit Breaks in the Upgrade Menu. You can do 4 Limit Breaks before and another 4 Limit Breaks after evolving a character, resulting in a total of 8 Limit Breaks. Each Limit Break raises the level cap by 5. As the evolution raises the cap by 10, the highest levels you can reach is level 90 for 4* characters and level 100 for 5* characters. 3* characters are unable to evolve, thus they can only do a total of 4 Limit Breanks, which also means the highest level these characters can reach is level 50.

To do a Limit Break, you need one Limit Break Item of the respective rarity and class (as well as some gold, but this should not be the problem). You obtain these from summoning a character repeatedly, or you can get them from the Trade Shop. For 5* characters, there are not only Limit Break Materials corresponding to the classes, but also Materials that correspond to the series they are from. (There is also a third type that can be used on any 5* character, but as this requires you to pay real money (and they are not worth the money, I omit further information here.) All three types are totally equivalent in regards to doing 1 Limit Break per item.

Besides the character' level, the maximum level for the skill levels also increases by doing limit breaks. For more details, see here

Evolving the Character
When a character has done 4 Limit Breaks AND reached the current maximum level (which is level 60 for 4* characters and level 70 for 5* characters), a character can evolve (vie the Upgrade Menu). Evolving does not only raise the character's level cap by 10, it will also change the card art of that character, the sprite that's displayed in the Room or when in battle, as well as the animation for the totteoki. (You can change these back via "Party" in the Main Menu.)

To evolve a character, you need a variety of Evolution Materials (as well as some gold, but this should not be the problem). There are 2 groups of Evolution Materials: For each of the 6 elements, there is a total of 5 different Evolution Materials, and for each of the 5 classes, there is a total of 3 different Evolution Materials. Depending on the rarity of the character to evolve, you either need the lower 3 types of elemental Material and the lower 2 types of the class Material, or you need the higher 3 types of elemental Material and the higher 2 types of the class Material.

Unlike Limit Breaks, evolving a character does NOT raise the level cap for the skills.

=Other Upgrades= Besides the character's level, there are some other means to upgrade a character. In detail, you can also
 * raise the level of every skill
 * raise the awakening level
 * unlock and level the character's exclusive weapon (only for specific 5* characters).

Raising the skill level
By using a skill for a certain times, the skill level will raise bit by bit. By raising the skill level, the skill gets better, for example the amount of damage it inflicts increases or the amount of buffs/debuffs/healed HP increases.

At first, the skill level can only be raised up to level 5, but after doing all Limit Breaks, the character's skill levels can get up to level 15 (for 3* characters) or to 25 (for 4* and 5* characters).

Raising the Awakening level
By getting multiple copies (commonly referred to as "dupes") of the same character, the Awakening level increases. The number of copies needed for one Awakening level depends on the rarity. For an overview, see here. As you need to summon the character for several times, this is nothing to be aimed for actively (although there are some exceptions).

Each Awakening level increases the character's general stats as well as the cap for the totteoki level (but not the cap for the other skills). 3* and 4* characters can increase the totteoki level cap by another 5 levels via Awakenings, and 5* characters can raise the totteoki level cap by 10 levels! Furthermore, 5* characters get their Party Costs decreased by 1 with each Awakening level.

Exclusive Weapons
Specific 5* characters can unlock their Exclusive Weapons upon reaching level 100, which can also get leveled up and evolved. For details, see here: Overview of how to max an Exclusive Weapon.