I'm actually a bit surprised by this myself, but there really weren't a lot of stories about Batman getting transformed in World's Finest. The ones that are out there are pretty wild, but they're nowhere near as common as they were in Batman or Detective.
Batman's most common transformation in World's Finest was the obvious one: gaining powers comparable to Superman. It happened in World's Finest #77:
A crook invented a ray that would give anyone super powers for a day (and also a ray to take them away from Superman). This concept seemed to appeal to readers and so another story appeared 10 issues later:
In this story, Jor-El (Superman's father) had planned to send a bunch of super-power granting pills in baby Kal-El's rocket ship, but he forgot to include them, However, like everything else from Krypton, it eventually made its way to Earth, where it was inevitably found by a crook named Elton Craig. Craig used a pill to make himself powerful, and the Kryptonite lining the box to incapacitate Superman. Supes is able to melt the green K with the heat of his x-ray vision, but he foolishly decides to take one of the pills.Turns out there is a tiny bit of green K in the pill and he will be without powers for a day.
He gives Batman and Robin a pill each from the box, and so we sort of get scenes like the above. Actually the story is more initially about Batman and Robin being a little too eager to use their poorly controlled powers; it is only after Superman gives them some training that they use them correctly.
The next couple of transformations did not affect Batman. In WF #90, we got our first look at the Super-Batwoman thanks to Elton Craig having more of Jor-El's pills. In #93 a ray transferred some of Superman's intelligence to Robin, with the result that Robin became a genius and Superman was a bit slow on the uptake.
In World's Finest #95, an alien gives Batman super powers specifically so he and Superman can battle it out for a story. In classic DC fashion neither one wins conclusively. In #100, all three of them are shrunk in size, but it's just a Kandor story.
By this point (mid-1959) Schiff's name was appearing in the indicia, and there are the requisite aliens and monsters (not entirely inappropriate given Superman's involvement in the stories), but the transformations remained not weird and fairly rare. Batman gained some superpowers in WF #109:
Super-Batwoman made her second and final appearance in WF #117. Finally in World's Finest #121 we get our first genuine weird transformation of Batman in that mag:
While battling some crooks in an antique shop, Batman accidentally falls through a mirror into another dimension. When he returns, he is distorted and has unusual powers:
It's a truly wacky story. When Batman fell into the other dimension, an alien rebel assumed he was a monster summoned by the local tyrant and shot him with a raygun that gave him the oddball powers, but Batman instinctively made his way back to the mirror and got back into our dimension, although he had lost his mind on the return trip. Robin and Superman get the mirror back from the crooks, and figure out how to go into the other dimension, bringing Batman back with them. They convince the alien rebel that they are not on the tyrant's side and he agrees to restore Batman to normal after they help depose the tyrant. We do get a pretty amusing panel of a distorted Supes in action:
In WF #128 we got a pair of weird transformations for Batman:
Batman suddenly undergoes a series of transformations. The first, shown above, has him creating foam via a ray from his eyes, which eats away at concrete. The second:
What do you mean, "like?"
The third one is a little oddball--when some crooks throw green Kryptonite at Superman, Batman tries to save him, but discovers that he is weakened while Superman is unaffected. What is going on here?
Well it turns out that Superman had been engaged in his usual task of protecting Earth from comets, asteroids and rogue planets. Somehow he was affected so that when he shook hands with Batman later, his vulnerability to any type of Kryptonite was transferred to Batman. As it happened, Batman had some red K in his lab, which now affected him. Fortunately both effects wear off eventually.
In WF #131 there is this:
But although it's highlighted on the cover, it's only a couple panels in the book and they quickly recover.
And that's basically it for Batman's weird transformations in WF during Jack Schiff's five year official tenure as editor. It's pretty mild compared to the treatment Batman got in Detective. That's not to say that Schiff abandoned his usual trio of aliens, monsters and weird transformations, it's just that he emphasized the first two more in this particular book.
Weisinger took over with World's Finest #141, the May 1964 issue. For the most part he kept away from the weird transformations except for this one:
Weisinger was a big believer in our chrome-domed future.
I am not aware of any weird transformations in the Batman solo stories from World's Finest #2-70 or World's Best #1 although I wouldn't be completely surprised to find one or two.