Yeah, you only need two elements which makes this kinda easy all things considered:
1.) the level
2.) the fighters
That's it! The level is going to be just a room background (or more than one arena to fight in), it needs a floor (this can be y-value if the floor is straight or a vector if you want an angled floor) and the left and right walls (these are usually just x-values so they are straight). The background, the floor and the walls are your arena and that's all you need. Your fighters are standing on the floor, they can't go further left than the left wall and no further right than the right wall. The background image is purely cosmetic.
Handling the fighters is more complex, you would use characters of course and then just have them play their proper animation when you hit a button. Move them to the left or right when walking, have them move up and down when jumping, a combination of both movements for diagonal jumps. Check if the arm of the attacking fighter reaches into the sprite of the other one to determine if an attack (like a punch) hit or not.
That's the basics that you can see working in the game I linked!