The first five introductory rounds are simple enough for you to grasp the concepts of how the game works. You'll be able to earn a bunch of achievements on the list in these few rounds alone, and you'll be making trips back to the first two rounds for more difficult achievements later on.

Round 1 Round 1 starts you off with four enemies. The three red ones with goggles are called Pooka, and the fire-breathing dragon is a Fygar. The Fygar are the more dangerous foes since they have an actual attack, not to mention a ranged one. There are also two rocks in the level; dig under them and step out of the way before it falls, and the rock will drop down, killing everything beneath it. Doing this twice will make a Carrot pop up in the middle of the stage. It won't sit there forever, so get to it before it disappears for an achievement. For most stages, dropping at least two rocks will warrant some kind of food to pop up, so try to do this whenever you see a new achievement related to a round from now on.

Another good move to learn here is to use your harpoon on an enemy so you can pass right through it. This is going to be a very useful tactic for later levels, so it's a good idea to get the hang of it now. When you come across an enemy, just pump him with your harpoon three times (four will kill it) and then walk through the enemy. Once he deflates back to normal, he'll soon chase after you once more. Defeat all enemies however you feel like it to finish the round.

Carrot Obtain the Carrot that appears after dropping 2 rocks in a certain Round.

Carrot

Round 2 The second round already looks a bit different, and now there's a second Pygar to deal with. Deal with them however you please, but remember that there's a Turnip to find after dropping two rocks. You can always come back to this specific round later with the Round Select feature in the menus.

Turnip Obtain the Turnip that appears after dropping 2 rocks in a certain Round.

Turnip

Round 3 The enemy count is the same for Round 3, but the Pooka are pretty close to the starting position. It's a good idea to take them out first since they're so close to you, and just worry about the Pygar when they come after you. You can also pick up a Mushroom on this round for another achievement.

Mushroom Obtain the Mushroom that appears after dropping 2 rocks in a certain Round.

Mushroom

Round 4 Round 4 is set up nearly the same way as Round 3. Deal with the closest enemies first, and things should be fine. With enough enemy management, you should be able to drop two rocks for a Cucumber too, but make sure there are at least two enemies remaining if you're going for it. If there's just one enemy on the screen, he'll try to leave the area in surrender, which will end the round.

Cucumber Obtain the Cucumber that appears after dropping 2 rocks in a certain Round.

Cucumber

Round 5 Round 5 looks a lot different than the previous four, as there are now soil layers created in the ground. These don't impact anything, but it's a lot cooler to look at than just plain yellow dirt. They've also added another Pygar to spice things up. It's a good idea to head for the two Pooka to the left first due to how close to the starting point they are, then go in for the rest of the enemies as they get to you. Or, you can dig towards them if you don't feel like sitting around. You won't have to deal with rocks here, because Round 5 gives you a Cucumber, which is of course more easily obtained in Round 4. Source https://www.trueachievements.com/game/Dig-Dug/walkthrough/3