I think the idea is fine but the implementation should be adjusted.

Maybe have each test be you alleviating one of Nessie's worries so she eventually concedes, rather then you using things like intimidation to try and pursuade her. Which in this situation would probably do the exact opposite of help your case here. Youre basicly confirming to her that you are a threat rather then debunk it.

It would make you think but still give you ways to pursuade her; some might be more effective then others. For example if she mentions the former druid making an exact point it might be a good start to drop some of the quests as you are making the same point her master did. Some points might not need a test while others (like pursuading her that you arent a threat) might be. Then they could make that one hard to be convincing like it should be but make the rest irrelevant or even easier. That said easy tests can still fail and with RNG arent optimal. I think personally that 1 or 2 tests there or 1 if she notices you make the same point that the missing druid did would eleviate her worries. Or at the very least ease the conversation enough that outright tests arent needed to make your point. Sometimes less is more and I think that applies here.

Now its just a stack of test that you have to complete and what options you pick doesent seem to matter. Which basicly means that 999.999 out of 1.000.000 times you end up having to attack her.