I did it by allying+RM five electors and boosting diplo reputation with the diplo idea groups, policies giving +1 rep, advisor and the control of ivory trade (on the African coast).
By the way in my last game the Catholics lost the League War... well actually the Catholic Emperor lost but four of the five Catholic major powers (France, England, Commonwealth and Portugal) were part of the Protestant League. With most of my army being overseas, I was able to defeat Portugal (and win 4 provinces) but the French in the meantime conquered Germany and the Emperor surrendered before my armies reach the area.
So to have the achievement, I switched to Protestant. I became Emperor when the first protestant Emperor (Wolgast, so not a big country) died, but found that the HRE was a mess. I spent the next two decades converting catholic and reformed princes to protestant and retaking provinces held by non-HRE members.... and then my heir and my emperor died in 2-3 months, and I lost the throne to... Austria, that had switched to Protestant too ! (I had not been able to unlock the mission for PU Austria due to zeal blocking conversion in
By the way, at this time I also realized that to finish the Spanish mission tree (another achievement), I have to create Holy Orders in America... and only Catholic can do that. So I switched back, and rather than be Emperor and push to Erbkaisertum, I destroyed the Empire. I was still allied with 5 electors, and the two remaining were allied so attacking one drew the other and the Emperor in the war, I just had to take all three capitals and boom. By the way I switched back to Catholic just before the war so the -100 prestige for switching was "cancelled" by the +100 prestige for destroying the HRE.