If you want to do fully predesigned levels, you can pick up something like the tiled level editor and use that to design all the levels. Then matching sprites to put on the screen as the player moves on the level.
But I would guess something like the Oswald you linked would not be made like that. Rather track the player progress and put different types of items on the screen depending on how far he is.
Anyway, depends on what types of levels you want. Fully manually designed, always the same, ends somewhere. First option. Never-ending with variation, second option. Or mix however you like.
