First and foremost, as you start a new world you should always pick up any available quests, especially Prospector Zeke's quests. Zeke can be found around the Spiral Door of every world. For Krokotopia Zeke is situated in The Oasis.

The First Oasis Beetle can be found behind the Deck and Robe store to the left of the map.

The Second Oasis Beetle can be found to the right side of the Krokotopia Library.

The Altar of Kings Beetle can be found at the lowest point on the stairs to the left of the Altar of Kings.

The Chamber of Fire Beetle can be found on the second highest level of the Excavation Site.

The Sphinx Island Beetle can be found behind the giant Sphinx.

The Entrance Hall Beetle can be found at the top of the steps outside of the Vault of Ice enterance.

The Emperor's Retreat Beetle can be found on deck opposite Shalek the Wise in the frozen lake area of the Emperor's Retreat. To access this beetle you need to defeat the first two bosses in this dungeon to unlock the door to the lake.

The Tomb of Storms Beetle can be found behind the Sphinx Head/Portal to the Oasis on the Well of Spirits Island.

The Well of Spirits Beetle can be found on the second level, behind the main Krok statue.

The Karanahn Barracks Beetle can be found on the furthest island, at the entrance to a small building.