After completing the game the credit sequence has finished continue playing.
In the Dragon Fountain press A to play the New Land dungeon
Mountain Level:
Complete the Light House Level.
Bat Spear:
After completing the first level you get to the Circus Level.
Encounter every enemy there except the Boss. The woman at your house will then buy you the Bat Spear.
You will find it in the Hero selection in the closet.