To upgrade the mastery level of your plants, pay attention to the graphic over the plant when you harvest it.
The graphic will say something like "Grow 5 plants with 15 buds".
This requires you to maximize your yield for the plant you're trying to upgrade.

An image of the Afghani Mastery screen

To do this you must set the temperature of your A/C at the proper setting for the plant, water it at the correct time intervals and install a light over the plant.

An image of the AC temperature screen.

To get to the higher mastery levels you will need to upgrade your lights. Don't use fertilizer on the plants you are trying to increase your mastery level on as doing so eliminates your temperature bonus, which you need to maximize your bud yield.