The Menace of the Mallrog

 is the third level. Completing it unlocks Nikola Tesla.

Reach Dog Tiara Store without being hit by a Heart Attacker
Reward: XP Difficult, due to the number of Heart Attackers. Try using a ranged character to take them down or Dash out of the blast radius with a melee character.

Find the hidden treasure
Reward: XP

Escape without anyone being hit by a Heart Attacker
Reward: Archimedes' Sponge Difficult, particularly for melee characters. Julius Caesar makes this challenge quite easy with his secondary mode.

Destroy 100 shopping bags

 * Reward: Davey Jones' Locker

Self-explanatory. At this point, it'd be tougher to convince you not to destroy them, eh?

Don't get killed by the Mallrog

 * Reward: 461 XP

Can be difficult with certain characters. Ranged ones, like Julius Caesar or Queen Elizabeth I will find it easier to survive, melee characters have their work cut out for them.