The Joker often likes to proclaim himself Batman's greatest nemesis, helping the Dark Knight grow ever more capable in his war on crime, but the evidence proves otherwise. Joker is too chaotic to be responsible for Batman’s growth - though he tends to critique Bruce Wayne's worldview, the hero almost always wins through existing tactics, especially the trust he places in his allies. However, this is another villain who actually seems to help Batman evolve whenever they clash.
It is an undeniable fact that Batman and Joker share an unbreakable connection. Both were created by Bob Kane and Bill Finger (as well as Jerry Robinson, for Joker). With multiple live-action adaptations to their names, the two characters have grown past their comic origins to pop-culture superstardom. Non-comic book readers all over the world know that Batman and Joker are enemies. The two go together like peanut butter and jelly. But when it comes to developing Batman as a character, he and Joker are stuck in an endless loop with no real growth - no matter what the villain says to the contrary.
The Joker often states it’s his ability to make Batman the best hero he can be that makes him the Caped Crusader’s greatest nemesis. This goal was the driving factor of the 2012 story arc "Death of the Family." Primarily running in Batman #13-17 with tie-in stories through Bat-comics like Nightwing and Batgirl, "Death of the Family" focused on Joker attempting to take out members of the Bat-Family as he believed they were making Batman weaker by giving him help. Joker argues that he's the one constantly testing Bruce and making him stronger, but while he does often push the Dark Knight to question his methods, Joker stories tend to depict the exact opposite - Joker pushing Batman to go further than his morals allow, but failing to actually change his methods or connections to others. Even when Joker killed Robin, Batman eventually got a new sidekick and carried on in the same style. But surprisingly, Joker's claim is actually true of another villain: Darkseid.
Darkseid has forced Batman to up his superhero game ten-fold, and he does it reliably. Primarily a Justice League villain, Darkseid has nevertheless faced Batman individually several times, and each time, Bruce Wayne radically adapts his perspective. In Final Crisis, Bruce finally breaks his lifelong ban on firearms to kill the New God of Evil. Flung through time by Darkseid in response, Bruce travels through different eras that test his resolve and skills while hugely increasing his bond to and understanding of Gotham City. Bruce later starts the worldwide team Batman Inc., partly inspired by operating as Batman in different time periods, and by Dick Grayson's ability to fill in for him while he was away. Darkseid also inspired Bruce to pilot perhaps his most impressive suit ever, the Hellbat Armor, when he stole the body of his son Damian.
Each time Batman clashes with Darkseid, the scope of his mission expands, or he embraces technology or tactics he's never used before. Joker might wish that Batman's evolution could be laid at his door, but the evidence suggests that Darkseid is the villain who actually forces him to grow. It's even a pattern that seems to be true across the multiverse - in the potential future of the recent Justice League: Last Ride #7 (from Chip Zdarsky and Miguel Mendonca), Batman goes from thinking the League should disband to expanding it into a universal operation, citing Darkseid's evil as his inspiration.
No one can ever discount Joker’s influence over Batman. He has succeeded many times in traumatizing Batman in ways few ever have. But rather than challenging Batman to grow as a hero, Joker is more responsible for torturing him in an endless cycle, testing his resolve without truly demanding growth. Joker would hate to hear it, but it's Darkseid who really forces Batman to be the greatest hero possible.