There are two types of enemies in the game: There's the round and red Pooka, which wears yellow goggles, and there's the fire-breathing Pygar. Both enemies can slowly phase through the dirt to get to you more easily, so there's really never a safe place in any round of the game. As you progress through the rounds, enemies will become faster, making running away less and less of a viable option of staying alive.

Feathering your attack and moving in a direction towards the enemy you're attacking will cause you to attack the enemy faster, meaning that you'll be able to kill your adversaries faster. Try this out when you can; you won't have to depend on it as you play the game, but it sure helps. Source: trueachievements.com/game/Dig-Dug/walkthrough/2