You will never get a fine point with this pencil, and it is quite fragile. I use a NYX sharpener, and it suffices.
I use my Urban Decay sharpener, which works with nearly every pencil. This lip liner, however, is very soft and doesn't like to be sharpened. I'm always a little afraid that the tip will break off, so I don't sharpen it too often or aggressively. Unfortunately, I'm not able to get it to a sharp point, but I'm able to do a good enough job that it hasn't broken and is still very usable.