Dead Eye Plankton is a plankton (hence his name), that is short and green sharing an exact resemblence to Plankton featured on the show Spongebob Squarepants. He is about 2 inches tall with one uni-eye and a moustache with a top hat and a whip.
Besides the fact that Dead eye is wearing western clothes. Dead eye was one of the many ancestors of Plankton. Which is another villain. He was featured in the episode "Pest of the West". He is a bad cowboy (as you can say) in 1800's trying to take over the town of Dead Eye Gulch (which was now named Bikini Bottom).
Dead eye's goal was to own the town and run Krabs out of business like his 200 year younger relative, Plankton, did. So he first started by invading the Salon and running Krabs out of business. Although he was only 2 inches tall, everyone was still afraid of him.
He forced the whole town to then be under his control and pay him very unreasonable taxes including personal belongings. Soon afterwords Spongebuck came back into town after he got kicked out and accidentally challenged a duel with Dead eye at 12:00 pm.
So Dead eye and Spongebuck had their duel but Spongebuck accidently stepped on dead eye and then everyone noticed that he isn't as powerful as he seems and stepped on him and threw him in jail.