Ultimate Ninja's Initial Goal?

[The Terror of Death]

I never really thought about it, but upon seeing season 2 again it's really confusing. He initially wants to make a name for himself by beating Earth's greatest warrior but how does that help him in the long run and why did he choose Leonardo?

- Splinter won the previous Battle Nexus, so wouldn't he technically be considered Earth's current best warrior?

- It was shown in the hall of champions that Shredder won the previous tournament multiple times, but it was never actually stated which one(s). It could have been the Tribunal, the original Saki, or even a Shredder from a different universe.

- If Chrell did in fact win the Battle Nexus, there are still plenty of other fighters who accomplished that feat. Why did he specifically plan on defeating him and not someone from a different planet? Was Shredder the most notorious fighter in the multiverse?

- The fight between Leonardo and Shredder involved several people and wasn't even a sanctioned match with rules, so how can it be considered a real victory?

- Would anyone even care if he beat Leonardo? Few people knew of Leonardo's existence and even less should know he beat the Shredder. Does the Daimyo have some intergalactic tv channel that livestreams the best fights?

- His true/second goal was to dethrone his father and take his war staff but how would defeating Leonardo help achieve that beyond giving him a small ego boost?