From the Super Mario Wiki
(Redirected from Mega Deep-Cheep
A Big Deep Cheep is a large Deep Cheep that appears in New Super Mario Bros., New Super Mario Bros. Wii and New Super Mario Bros. 2. It swims along, and if Mario or Luigi come too close, they will chase him. Other than that, they act the same as other Deep Cheeps, despite being much bigger.
A Big Deep Cheep
and its smaller counterpart in New Super Mario Bros. Wii
In New Super Mario Bros. Wii, their size has been reduced so they appear to be just slightly bigger. However, in New Super Mario Bros. 2 they regain their original size. They also appear in New Super Luigi U with their smaller counterparts.
Big Deep Cheeps are set to reappear in Super Mario Maker. They can appear if the player puts a Super Mushroom on a Deep Cheep, however they can't chase the player due to the normal green Cheep Cheeps, and the Blurps are unable to chase the player.