It actually took me a long ass time to understand what to do on Augusta and what her meters are. Your goal is to fill the bottom Majesty meter (maximum 2 points) in order to use her Enhanced Ult. You get 1 stack of Majesty essentially "for free" (will explain later). The 2nd stack of Majesty can be gained when you use her Enhanced E combo.
To use her Enhanced E combo, you have to fill up the middle Ascendancy meter. You can do this by 3 ways.
>Normal Ult (no energy needed, it's on a cooldown only) by tapping R
>Regular E
>Normal attacks (you spam these after you've pressed R and E)
The purple Prowess meter lets her do Enhanced Heavy Attacks, which just lets you do more damage on the way to building up the Ascendancy meter. Prowess is also full after you Intro into Augusta, so you can start with Enhanced Heavy Attacks right away.

So the rotation is Ooga Booga (tap R, E, left click until middle meter is full) > E + E + E > hold R (not tap) > mash left click until ult animation.

You get the free stack of Majesty at the beginning by being out of combat for 4 seconds. During combat, you're going to Outro from Augusta into your support, most likely SK/Verina, giving them an Amplify Buff. If you Outro with SK/Verina before Augusta's buff wears off, she gains 1 stack of Majesty. DO NOT SWAP OFF SK/VERINA UNTIL YOU OUTRO WITH THEM, and don't take too long, as the buff lasts 14 sec.

Augusta has 2 kinds of enhanced heavy attacks. First one is be on ground, hold left click, then release and mash left click. The other method is to press jump for a jumping uppercut. The jumping uppercut can also occur if you did a regular Heavy Attack, that attack filled up your purple forte, and you pressed left click immediately after.