The boss unlocks automatically as soon as you enter level 3-2 for the first time. You should see him flying around the world map, near the castle, at that point.
The Devil is stationary, but he has a large amount of HP, a swipe attack, and the ability to raise lava from the ground and have spikes fall from the ceiling.
This is an endurance battle more than anything: keep jumping on him and getting out of the way before the spikes fall onto you, getting out of the way before the lava raises.
When his HP starts getting low, get ready to jump back onto solid ground so you don't fall into the pit below.
Defeating the boss unlocks a trophy and grants a large amount of experience points.