1. Start off by selecting the Third Crusade start and select the Kingdom of Sicily. Turn on Ironman and you're ready to start the game.

2. You'll have a lot of territories in your demesne. Try to get a start that gives you at least five demesne counties. Start off by giving the County of Bari to the Duke of Apulia. Make your capital Napoli or Pallermo, then give two of the Sicilian counties to their respective priests along with the rest of the Sicilian counties.

3. Set the Investiture Law to free. If playing with Conclave, you'll need to request support from enough council members to pass the law as you will need it relatively soon.

4. Your next goal is to convert your culture to Italian by right clicking your character portrait. (Note: This is only possible with the Rajas of India DLC. Otherwise you will need to have an heir educated by an Italian with the diligent trait which will take time. Having Italian culture is incredibly helpful with getting this achievement.) For this you need 500 prestige and you preferably want to do it before your wife gives birth to a male heir. To do that you will need to create the Duchies of Sicily and either Capua or Salerno as creating the Duchies will give you 200 prestige apiece. This costs roughly 400 gold total to do, but you don't need to take a loan from the Jewish Merchants to do it as you should be racking up anywhere between 30-50 gold a month from taxes. You'll have the gold in no time. You should set your focus to theology to get more chances to earn piety. Now you are ready to unpause the game.

5. When you create the Duchy of Sicily, you immediately want to give it to one of the Prince-Bishops as this will give him a very high secular power to get elected to the College of Cardinals. It is unlikely for the first priest to be the one that will be getting you the achievement though which is why you need Free Investiture.

6. Sometime during all this the Pope will declare a Crusade. Usually this will be for Andalusia, because why should the third crusade target the actual location of the third historical third crusade? That's just silly.
Anyways, join the Crusade and send all your troops to the country being attacked. You mainly want the bonus prestige, piety, and gold that comes with the crusade.

7. You should soon have enough prestige to convert to Italian culture. Do it as soon as possible. Once you have changed culture, spend all of your piety inviting holy men to your court. You want to make sure you are Italian before inviting the holy men as Italian's get a +200 bonus to the College of Cardinals and their eventual Papal suitability. Then go to the religion tab to select who should be the heir to your Prince-Bishop friend. The person you select needs to have at least one sin (traits with a red background), with the more the better. They also need 2 or less of both intrigue and diplomacy. High learning learning helps, but low intrigue, diplomacy, and sins are the most important. Being young is pretty useful as well as you need him to survive long enough.

Credit: Quendorsof has informed me that "a bishop being a lunatic, cynical, possessed, homosexual or hedonist will also work."

8. Once you have selected the heir to the prince-bishopric, you want him to start leading your crusade troops. Then start besieging county capitals with your army. Every county capital you siege in the crusade grants the leader of the siege +100 prestige and piety, which will give your heir a nice little bump that will push him ahead when it comes to be election time. So siege the capital then move to the next one. Try to keep your troops away from those of your allies so that their commanders don't take over as siege leader.

9. Once the crusade has ended, bring your troops on home. The original Prince-Bishop should hopefully have died by this point. Either assassinate him or wait for nature to take its course so your chosen successor can take the throne. Make your new Prince-Bishop court chaplain and send him to improve religious relations in Rome, which will grant him another +100 bonus to getting elected. All this should push him far ahead of your other vassals' bishops so that he should easily be your best cardinal candidate.

10. Pause the game. Put enough money into his election fund that he is at least over 100 ahead of anyone else who might be trying to get their candidate elected. (IMPORTANT NOTE You must put at least ten gold into his election fund, otherwise it will not count as you having funded the priest and the achievement will NOT pop even if he gets elected.) Now you just have to wait on someone to die, although you can always plot an assassination in an attempt to force your guy's way in early. If you have Monks and Mystics, joining the Satanists or the Assassins would be a good way to take out a few obstacles in your path.
Also note that if your ruler dies after the priest becomes a cardinal then it will not count toward the achievement. You will have to start the process over.

11. Once the priest develops the Wicked Priest trait he should still have enough secular power that the others will want to elect him (in my tests the secular power, Italian culture, and being in Rome got him +510 Papal suitability), but you might need to to take out a few people on the way. This used to be a lot easier back when there was an assassination button. Now you just have to keep plotting against the preferatus until your guy is on top, which takes time. No more killing the pope and half the college to force your guy to ascend. To further increase Papal suitability, you can give your Cardinal more titles and grant him county level vassals which will increase his secular power.

As a potential alternative I have been informed by noxbestia that once a bishop that you have funded has been elected to the College of Cardinals you may turn him into an anti-pope and press his claim, earning the achievement. Some people have reported that this works and other people have reported that it does not work. Personally I earned the achievement through waiting for the old pope to die and my guy to be elected, so I would recommend that method.

13. That's it. Your Wicked Priest should now be the Pope. Beware though, the Wicked Priest might amend his ways and lose the Wicked Priest trait upon his ascension to the Throne of Saint Peter, ruining all of your hard work and preventing you from getting the achievement. You just need to be willing to start over from scratch if you really mess up.