At certain portions of the game, there are plenty ways to level up fast.
One of them is the dangerous lavamen training within Mount Zublo. By using fire element attacks on them, their power grows as well their experience.
Precation is taken by gaining the means to render fire attacks harmless, as such aquirring two magma armors and one fire ring is recommended, as well buying many ammonia as the battle will take time.
In order to lower the chances of being KOed, the defense formation should be used, alongside casting shield on the group before starting to apply fire on the lavamen.
At the start, you rather do not want power up many lavamen at once, so if you encounter more than one, focus on one before you go on the other.
With growing defense (steal proteins from the Volcano Rocks), you increase your chance to survive direct hits more easly.
At one point lavamen will have extrem high defence, as such using Momo with Spirit Blast, to either harm or power up lavamen is recommended, when AP is low.
Other places to level up are the container yard. Archmages (42.000 exp) and Berserkers (30.000 exp) have high exp awards as well some good loot to boot.