The problem is that OP did not give a tech level.
For calculating resistance, supercavitation makes it really, really hard. Next to impossible without actual testing. And before you say this speed is impossible for submarines: it was attempted in real world in 2009 and it still looked promising in 2016. Is tech supposed to be limited to 1986 Akula-class tech, as Akula is mentioned in the question?
2 person requirement is imprecise as we do not know how long such submarine should support them - and without tech level we have two big unknowns about required size of a life-support system. Privately built requirement suggest some limitations to availability of stuff to private citizens, but we don't know what it is.
Last line of the question asks for maximum depth, not speed, so it is unclear which one OP is really asking about.
Last but not least, it is quite possible that OP is not even building a fictional world, but only curious about limits in our world. That would make his question off-topic.