If I recall correctly you are limited to 64 sprites (8x8 pixels) on screen and 8 sprites max per scan line. If you have more than 8 sprites flicker will occur. So if your character is 16x24 pixels you are already using 6 sprites + sprites you might use as projectiles for shooting your enemy.
But you can use a trick and use the background tiles as part of your enemy. I couldn't find it, but someone on the forum made a giant spider and used sprites only for some parts of the spider.
EDIT: Here are two examples from Arielle and Ninja Gaiden 3