What's the fastest way to level up?

You'll get XP by hitting enemies. One hit stands for ~1XP on insane ~2XP. If you deal less damage it still counts as 1 hit. So when you have low strength you can hit the enemies more times thus getting more XP. You wont get XP if the enemy is already dead (but you can still hit them). In arena you wont get XP either.

A formula to calculate XP needed for the next level:

XP for NextLevel = (CurrentLevel x (PrevLevel x 20 + 380)) / 2

The Industrialist and the Fencer have a multi-saw-blade attack that hits multiple times really fast. You can level them up really fast by just spamming magic.

(unlock with Blue Knight)

I already know that the Giraffey pet can help to level up faster (10% xp bonus),

This is true and will get you more XP by equipping him.
There are a few ways to level up fast.

Using the boomerang glitch on Industrial Castle. Throw the boomerang behind one of the standing poles when they come up. The boomerang hits many times per second. On insane mode you'll get like ~10.000XP.

Defeating infinite spawning trolls on Troll boss on insane mode. This is a good way if you know how to juggle and have low strength. XXY/SST* or XXYY/SSTT* across the screen will grant you ~20.000 a run. Try not to kill the boss. I've heard about people getting over 50k with this method.

(*) XBOX: X = X, Y = Y| PS3: S = Square, T = Triangle