out of batman's villians, who is joker's biggest rival?

Hush was the first that popped in my head. He's smart and a little crazy.

Riddler is the greatest challenge for Bruce's mind, critical thinking, and Detective skills.

Bane is a challenge for his mind, skill, and willpower.

Two-Face challenges his morality and conscience, since Batman is part of the reason Harvey is Two-Face.

Ra's is another test of skill and morality.

It goes on but every Batman villain challenges Bruce differently by making him use a specific skill or skillset. For example Joker is a matter of conscience, morality, and sometimes (but not always) problem solving/critical thinking. Overall Bane is probably the biggest threat, but it really depends on what you're seeking to challenge Batman in.

Ra's al Ghul

Riddler is the greatest challenge for Bruce's mind, critical thinking, and Detective skills.

Bane is a challenge for his mind, skill, and willpower.

Two-Face challenges his morality and conscience, since Batman is part of the reason Harvey is Two-Face.

Ra's is another test of skill and morality.

It goes on but every Batman villain challenges Bruce differently by making him use a specific skill or skillset. For example Joker is a matter of conscience, morality, and sometimes (but not always) problem solving/critical thinking. Overall Bane is probably the biggest threat, but it really depends on what you're seeking to challenge Batman in.