What you need:
-Be catholic
-Have a priest with the Wicked Priest trait
-Money
-Free investiture
-Willingness to throw away a game where you already have money and power

What helps:
-A vassalized pope
-Lots of land
-Lots of piety

1st things 1st, you need to get yourself a vassal wicked priest. Don't bet on getting one randomly for cardinal election, explained in the next section.

To find the Wicked Priest you need to know what fires the Wicked Priest trait. The description says that the Wicked Priest is not only sinful but is also clumsy at hiding his sins.

To find a wicked Priest you need to search chars - > Vassals : Only men; Not married ; Ruler Yes ; My religion Yes

Now sort by lowest Intrigue first and look at the bishops. The Wicked Priest trait is a black circle with a cross in it. Check that the bishop is your direct vassal, if not give him a county or duchy, so that he is.

If no Wicked Priest was to be found, go to the Religion menu and start working on the successions. Appoint successors to the bishoprics that are all close to zero intigue and have as many sins as possible (the one I had had only 2 sins and a virtue too, I think sins>virtue is the only criteria).

Start killing of the non-wicked priest bishops (high intrigue, not sins>virtues) and set the game speed to high. Monitor the bishops if in 10 years they are not wicked priests scrap them. I have no idea how long it takes to get the trait, it seems to be really random. Soon you should have a Wicked Priest (soon as in in the next 100 years).

This is the hardest part of all:
You cannot choose who your best bishop for cardinal is AND the wicked priest has almost no chance by default. You don't even know how much the differnce is between the WP and the current candidate is.

Lets look at the points:
Opinion with lieges: Seems to be your opinion of the bishop and the opinion of e pope of the bishop multiplied by 2 or 1.5 or so. Does not really matter. Most popes will hate the WP as they hate all sin. Most rulers are also more virtuous than the WP, usually getting an opinion malus too. Unless the WP is also very diplomatic, this usually goes into the negatives, not much to do about it.
Piety: Sins give negative piety, WP gives 1.00 negative piety per month the WP won't win in piety over the other guys
Sins/Virtues: The WP will get negatives here too
Campaign funds: It seems the AI actively funds their bishops here, that does not only mean outside of realm bishops, inside too. A wealthy duke will net up to 800+ points for his candidate. This is the part where trowing away the game comes. You need to remove These priests from your realm, just killing them won't do any good, the funds are still there also the fresh bishop is likely a better candidate to boot. Give their liege independence or retract vassalage. Either way you will have to take these guys out of the game and for that either you make your vassals hate you or grant them independence. You won't have 200 years to revoke everything. The WP can die, also the WP trait can be lost. At best the WP is the only bishop in the realm, thus the only candidate, thus the best candidate.
-Being Italian nets a +200, which is great, but not everyone is italian, if the WP is than you only have to remove all other italian bishops from the realm

-Secular power: the most important one as you can control this directly. If you gave the WP a duchy, transfer every single count that you have under your direct control under him, also every barony, also every bishopric. This will give him a massive boost to Secular power and should make him the best candidate. The only problem there can be is Campaign funds, but if no duke has a candidate in your realm, than there should not be a problem.

With this you should have the WP as a candidate for Cardinal and by killing of one of the cardinals (look for the lowest int score and assasinate) he should be elected cardinal.

You have won. There really are no theocracies in this game by default. The chances for one forming are slim. There is no campaign fund in pope selection so your WP with 1000+ for secular power should win. If not conquer more land and transfer vassalage to him.