One of the problems that new players will encounter is a difficulty in understanding what side of an island will fall in the water, and which side will stay. The answer is simple: which ever portion is smaller. In practice this can be much harder to determine if it looks like you are splitting close to half of the island. This in turn leads to a lot of lost lives when you're still learning the game. In fact, if you are a new player, don't be in such a rush to use Dig Dug's new jackhammering ability. Rely on your pump to dispatch enemies, and practice using the jackhammer when you have spare time.
Learn the lay of the land
On your first visit to any island, try to take as much time to study it as possible. Concentrate on eliminating enemies with your pump, and try to leave at least two enemies until you are done studying the island. Look for ground pegs that you can take advantage of, and create landslides with. Once you have played any island at least twice, you should be familiar enough with it to execute your plan to create a landslide as soon as you start. If you miss the opportunity to do it early on, you may have to spend more time luring enemies away from the site and bring them back when you are ready.
Landslides are easier in the beginning
The early rounds are obviously easier than the later ones, and they are designed to maximize landslide opportunities. As you are playing further in the game, you will begin to notice that it will become harder to find an obvious landslide situation and you will have to become more creative. When you are familiar with the early rounds, take advantage of the easy landslide setups to give your score a nice boost. And don't forget, three landslides earns you a bonus vegetable which helps your score out as well. As you progress through the game, switch to relying on your pump for easier kills.
Cracks are your best defense
You should remember that unless Pookas or Fygars become ghosts, they cannot cross over the cracks. Even if you cannot necessarily use a peg to create a landslide, you can still use them to create cracks in the ground and generally make it more difficult for enemies to get around. In some cases, you can use cracks to break up a pack of Pookas that have bunched together. In other cases, you can create a "fence" of cracks, and leave one section alone as a "gate". Then you can lure all of the enemies behind the fence and close the gate by creating the last crack and watch them all drown in the sea as the point value you earned for doing so flies across the screen. Remember, however, that a determined enemy can become a ghost and begin floating over a crack very slowly. Always be on the lookout and never stay in one section for too long. Dig Dug is never totally safe.
It takes more skill than strategy to win in the later rounds. Landslide opportunities are severely limited, and the multitude of enemies start coming at you very quickly. You must use the pegs to create cracks that you can use as a line of defense. The enemies will gather together, and you may need to use the pump stall technique learned in the first Dig Dug (where you had to pump up an enemy to stall them and safely pass through them) in order to get away a lot of the time. When you put some distance between you and the pack of enemies, find a crack to stand behind and pump enemies from behind the line until one becomes a ghost. If you're fast enough, you can kill one enemy, and start pumping the ghost before it reaches you. If not, or if there are too many ghosts coming at you, you should prepare to run away, and find another hiding spot. Thorough knowledge of the island layout can help you set up two safety zones if you need to run back and forth, but you should always be careful not to accidentally run into any enemies.