None of these depend on luck to get the achievement. Luck could influence how fast you finish them within timeframe, but for sufficiently skilled players they could get pheasant strut + time gated achievements within timeframe reliably. Approach + outlook matter for stuff like this.
Edit: Lotharingia is bugged right now since you can't get female heirs. Doing it as original Marie is the only way, wish I knew that before passing that point.
How does the Pheasant Strut not rely on Luck?
1: You need Prussia to form. You are in India. For Prussia to form:
a: You need an applicable country [Usually TO or Brandenburg] to aquire the correct provinces and not die. ~95% of the time AI TO gets killed by a railroad event that throws them into a war that is only winnable if Poland's AI completely derps; and TO will be dead with it's cores long gone by the time you get there. Brandenburg requires Danzig to form Prussia; and Brandenburg [especially with nerfed ideas] is not taking Danzig unless; again; Poland completely fails. If the AI is to form Prussia you are RELYING on luck that Poland fails [Usually related to Poland not accepting the PLC; which is ~10%.]
b: The country that is forming Prussia HAS to flip Protestant or Reformed. If they stay Catholic;
tough luck!
c: If you're argueing the 'Brandenburg and TO can form Prussia while vassals' angle, yes, they can. But as stated in A; about 95% of the time; by the time you get to the region; TO's cores are gone. So you can't use TO. And you're Indian. So if Brandenburg or TO are Catholic; good luck making them Protestant or Reformed! It's not like you can enforce religion.
So this part is 100% luck based. The alternative is hoping they have enough wrong-religion provinces by the time you get there; and they fall to rebels. Which is still luck-based. Even if you Support Rebels; the rebels still need to be able to actually spawn. If they've converted them back to Catholic? You're screwed.
d: Brandenburg actually has to be small enough to vassalise by the time you get there. Also; if you're trying to vassalise Brandenburg; you gotta fight the HRE. And if you have to cut Brandenburg in the HRE down to size to vassalise; you're going to have to deal with coalitions as a wrong-culture; heretic religion that is attacking the HRE. This is going to slow you down heavily; and you already have to force your way to the HRE through either Russia or the Ottomans; which are a big enough blob that it's going to take a while simply due to truces. [Plus whatever power is in the Iranian region]
e: Finally; Prussia has to be strong enough so that they can field 100,000 men. Not their allies and Prussia. Prussia itself.
2: Again, you're a Nepalese minor. You can easily get screwed over earlygame if someone like Juanpur decides to kill you or Juanpur/Bengal alliance-bloc you in by allying your neighbours. You're not beating Juanpur if Juanpur decides to kill you in the first few years.