Before creating a enemy as character, you must think on his behavior in-game. Let's take a Goomba as example. Don't think Goomba as a brown fungus, but as a thing that walk horizontally and will hurt the player if touch on sides, but die if touch at the top.
When you're done, then you can think in the visual of the enemy, as it matches with his behavior. You don't need necessarily do this to all enemies, but it's a good tip.
Another thing is make he looks like he is actually the main villain's follower. For example, if the main villain is a king, then make enemies as knights. If the main villain is a wizard, then make minor wizards as enemies. You don't need do this to all enemies too.
But the best tip is, don't follow any of the tips before, unless you really want to. A good thing on a game is make it escapes from the reality. You can make a cute rabbit be a follower of a demon king. Why not? It's up to your creativity.
If you need some ideas, play some games, or even take a look outside of games. What frustrates you the most? What you would like to punch until the death?
These are my tips. Have a good enemy designing!