how did drps eyes get that way and how did she get her cutie mark!!!???

derpy hooves just has a lazy eye(that's super cute) and she is the mailmare of ponyville so her cutiemark is bubble wrap!=3derp

I think she was born with the lazy eye and learned to enjoy her difference. for the cutie mark either trying to impress her cousin dinky (that's how I roll) with bubbles, o bubblewrap!

she was born with a lazy eye ( which is super adorable!!) and Actually, Ponibooru once had an image featured that explained her cutie mark. It was one of the FIRST comics ever to be featured. Here is a summary though:

Derpy Hooves, a lost pony, rejected por the discomfort of her anterior homes, wandered the expanse of mountains, forests, and plains. The rain fell upon her lost soul, as night crept upon what she did not know was her last journey. Yet, a comforting presence appeared among the sorrow, the simplicity of bubbles. Oh, how they showed their sheen, even among the gloom of the darkening valleys, it had encantada Derpy to follow. As she laid pursuit to the rising bubbles, a great light lied on the horizon, banishing all that stood among her burdens. The bubbles, the enchanting yet minuscule bubbles... had guided her to her final, lovable, tolerant home... Ponyville. Peace... peace at last...

Derpy's eyes were a glitch in animación which they were going to fix until it became so popular so they decided to let it be thus Derpy hooves was born. AS for her cutie mark she was playing with bubble envolver, abrigo and it appeared tu can find the video on YouTube.