Back in town as Mouse-Man, you might want to heal your wounds in the hospital on the left, then save the game in the church.
Crossing the forest
Once you're ready, go outside of the town to the left, climb the 
Mouse-Blocks and continue to the left. Jump over the Fuzzballs. A Hovering Smog will drop flames on your way. On the first screen, the flames will simply fall on the ground and extinguish, but on the next one, the Hovering Smog's flames will chase you. The simplest way to get rid of the Hovering Smog is to use a 
Thunder or an 
Arrow. If you prefer to avoid the flames, either jump as they pass, or block them with your shield by facing them.
At the Mouse-Block maze, make your way to the top-left part of the screen and jump offscreen. You will arrive in a secret room with healing hearts and lots of money. Take the contents of the chest and get out. To reach the next screen, use the second passage from the top. Go through the forest until you reach a wall. Kill the red Willow Wisp to get a key. Go down in the water, climb the Mouse-Blocks and open the door. Open the chest to get a 
Heart Container. You can buy a Medicine for 291 gold in the shop. Don't go through the "Return" door yet, as you need to kill the next boss first! Get out of the room and climb the left wall. You will see a dungeon and a locked door. Continue climbing as high as possible, then jump off the wall and try to land on the platform. Enter the door before the red Willow Wisp reaches you. You will fall down if he does.
Finding and killing Dragon Zombie
You're now in Dragon Zombie's dungeon. Make your way to the top on one side of the dungeon, then fall down and climb up to the top again on the other side. Amongst the enemies you'll encounter, there are Willow Wisps. If you stay on the floor, they will move up and down, so they will be harder to hit. Walking on the ceiling will make them bump. Stay on the ceiling to kill them.
At the very top of the dungeon there is the boss' door. Prepare to fight Dragon Zombie and enter. Dragon Zombie will hide in the ground so that only his wings will stick up. He will move back and forth across the room. Avoid his wings by jumping over them as they pass. When he comes out of the ground, hit the dragon in the head. If you're too slow, he will start spitting poison at you. You can block it with your shield. After killing the dragon, take as much money as possible before touching the 
Blue Flame. It will turn you into Piranha-Man.