I unlocked the Arena a few days ago and have noticed that starting out I'm more or much more powerful than the chimeras in the arena but at lv30+ their stats become absurd. There is no way i, as a lv25, can beat something with 700+ defense and similar amounts of attack.

Is this intended or am I doing something wrong? Right now i only use the arena when starting a run and never again.

I think level scales to character's age perhaps. If I switch to someone who is 16 and immediately level them up, they still get very low-level enemies. And I noticed quests also are low level when the character is younger even after immediately leveling them.  I don't think it scales to level as, like you said, you can get enemies that are way higher than you. I haven't tested, and I'm not 100% sure, but I do know that I see asymmetries between character level and enemy/quest level and age seems to be the most likely variable.