Exactly what you need to know depends on the type of studio photography you are doing and the needs of the client. Generally, the more you know, the better you'll do. There isn't some set minimum or some set maximum beyond which it won't help.
Certainly basic composition and 3 point lighting are valuable to know, understanding the exposure triangle and depth of field is important. Understanding light modifiers will help you get the softness or harshness you want. But it all really depends.
There is also really no substitute for experience, which a college program can only minimally prepare you for. Shooting lots of photos is what most prepares you, college just helps know what traditionally has been considered good, but doing it is where you learn to do it.
Note I say this as someone who has been engaged in Audio/Visual work of all kinds (video, sound, photography, lighting, graphic design, etc) at some near professional or professional level for over 16 years. I also went to college for electronic media, arts and communications after I'd already been doing A/V stuff seriously for 5 to 6 years. I won't say that my time in school for that half of my major (I was a dual major.) was a waste, but it also was no where near as beneficial as my real world experience. It was beneficial in understanding the history and the whys of things, but most of the how was picked up from addressing problems in the real world.
Which I guess in reflection brings me to the most important skill you can possibly have. That is the ability to recognize what is wrong with your work and having the motivation and ability to discover how to fix it and do so. This is how you will grow and develop in the real world and if you can master this, it will help push your work to excellence.