Despite beat-em-ups being a very old genre with a lot of set conventions, documentation on how key parts of them work is surprisingly sparse. boghogooo on Twitter made this lovely set of diagrams mapping out a number of basic behaviors of enemies in these games. Many of these were established in Technōs Japan's Renegade (Nekketsu Kōha Kunio-kun) and proliferated throughout the genre for years.
Like many things in game design, this sort of thing is useful far beyond the genre they directly represent; maybe it will give you some ideas on how to make the enemies in your game work to challenge the player even if it's a completely different type of action game!
