I have already spent a lot of time in an excavator in my life and had to smile at the request. First question: How big is the mini excavator and how long did you rent it? With a 2m digging depth, it’s probably a 1.5-2t excavator, which won’t get you very far.
I don’t know if I even want to give tips here for safety reasons, but such an undertaking can basically only be done in layers, so removing 3 levels of about 1.7m each. Here you would need an excavator with at least 2.2m digging depth, otherwise you’ll need about 4 levels. It seems you understand sloping, but shoring will probably be enormously difficult, because how do you want to do that with the "small" internal dimensions and the great depth without suitable machines (a mini excavator is no use here)? You need a ramp to drive in and out. 30% incline is already very optimistic, as the mini excavator depending on the soil type might manage that, but you still need to get the soil out of the pit with a dumper or wheel loader, and they can’t manage 30%. How you want to get the soil out sensibly is not quite clear to me yet, because it’s all very tight, extremely deep and above all a lot. That will be a gigantic hole and I suspect you’ll need at least a week with the excavator.
Tip: Get a proper civil engineer with a 20t excavator. He’ll get the hole out in one day and will probably cost you about the same as renting your mini excavator for a longer period.
I could go crazy every time I see all the small garden landscapers who spend weeks doing outdoor facilities with their toy machines. And the clients still think afterwards how cheap it was compared to a civil engineer because the hourly wage was 30% lower. The work performance of a mini excavator compared to a real excavator is lower by a factor of 10-20; it simply can’t handle the volume. I use mini excavators for the final finishing touches when the rough work is done, foundations or places where big machines can’t get to. Everything else just costs a lot, a lot of money.