I am making batman-like character in the sense that he has a plan for everything. This includes knowing how to defeat even his allies. So, what are the weaknesses of every class that I could exploit? If you would like more specific classes, I am playing with an Illusions wizard, an ancestral barbarian, a life cleric, and a samurai fighter.

Really dialing in Batman Plans for a character requires specific knowledge of that character.  We can tell you what might, in general, work on those subclass archetypes, but it may well not apply to the specific people in your party.  That said, we'd also need to know what you're doing.  The plan changes drastically if you're Bat-Rogue as opposed to Bat-Bard, for example.

I would use this information in less "defeating even his allies" but more like "knowing their weaknesses so you can plan around them". Much better to go with a mindset of teamwork rather than killing each other.

With that in mind, down the list! (This is ignoring subclasses, cause I'm not going though each one, and feel free to correct me or add onto this. Also I haven't played half these classes so read this with a grain of salt) 
Barbarian, spells that aren't STR/DEX/CON saves.
Bard, melee fighters preferably one with counterspell/Mage Slayer.
Cleric, Mage Slayer? Probably just target Cleric first with very heavy damage?
Druid, . . . I need to think more on that.
Fighter, most average fighters can't deal with most spells.
Monk, monk relies on hitting and running before they are hit. Anything to disrupt their movement leaves them vulnerable.
Paladin, smites are mostly melee, keep them at range and prevent them from hitting smites.
Ranger, very subclass dependent, heavy burst damage before they wear you down too much?
Rogue, almost no options for crowd control. A lot of small minions.
Sorcerer, melee with mage slayer
Wizard, melee with mage slayer.

This advice probably falls apart in the last tier. Especially anything involving spellcasters, those get very difficult to fight against.

I am a ranger, if that helps. 

Hmm.  That limits your options, and almost demands that you find noncombat means of dealing with each individual.  If you're serious about this, then just about the only way it happens is with poison - and not basic-***** 1d4 PHB poison, but poisons that debilitate the target.  The barb and fighter both have excellent saves against poison though, so that leaves it up to a very iffy chance.  At 9th level you can pick up Silence, which is the only chance in any remote hell that you can bring down the casters in an open fight.

You may be up a creek, or have to settle for plans to escape rather than kill.

Natural 1s

Bards ... Silence or a mechanic that takes away their spellcasting, but silence is particularly tough for Bards, because they are all about sound.

I imagine most other spellcasters would be similarly nerfed with silence that can be maintained.  Once their spell casting is turned off, their poor Armor Class and weapons proficiency should be easily beaten.

For Paladins, I think you would want to take away their heavy armor.  Heat metal, rust monsters and stuff like that would be a good start.

For Rogues, I think truesight and slow or petrify would be pretty debilitating.

The real problem with Batman is that nobody admits he is both ridiculously wealthy and has a super power:  The ability to predict exactly which gadget he is going to need. I mean seriously, he goes up against superman and he has kryptonite.  He goes up against Freeze and he has anti-cold stuff.  He goes up against Ivy and he has herbicide.  Etc. etc. etc.   Some of it is obvious as in he knows it is a plant based crime, but othertimes it is "wow you just happened to have a grappling hook while going into the sewer?"

So, this is what you need:

• One of every single protective magic item, starting with resistance magic items for each damage type.
• One of each offensive magic item type - fire, cold, shock, etc.  
• One of each and every single non-damaging magic item, ready to be equipped at a moments notice.
• Magical belt that holds everything you own.
• The ability to de-tune and re-attune yourself to all 3 magical items in one hour.

Quote from 4yulming4 >>

I would use this information in less "defeating even his allies" but more like "knowing their weaknesses so you can plan around them". Much better to go with a mindset of teamwork rather than killing each other.

With that in mind, down the list! (This is ignoring subclasses, cause I'm not going though each one, and feel free to correct me or add onto this. Also I haven't played half these classes so read this with a grain of salt) 
Barbarian, spells that aren't STR/DEX/CON saves.
Bard, melee fighters preferably one with counterspell/Mage Slayer.
Cleric, Mage Slayer? Probably just target Cleric first with very heavy damage?
Druid, . . . I need to think more on that.
Fighter, most average fighters can't deal with most spells.
Monk, monk relies on hitting and running before they are hit. Anything to disrupt their movement leaves them vulnerable.
Paladin, smites are mostly melee, keep them at range and prevent them from hitting smites.
Ranger, very subclass dependent, heavy burst damage before they wear you down too much?
Rogue, almost no options for crowd control. A lot of small minions.
Sorcerer, melee with mage slayer
Wizard, melee with mage slayer.

This advice probably falls apart in the last tier. Especially anything involving spellcasters, those get very difficult to fight against.

As this notes, a mage is likely the best, for counter-mage operations and to target barbarians who would normally benefit from rage. BAD IDEA: barbarian wizard. Rage, then cast fireball. the idea being that a wizard with literally any HP is gonna be something to fear. If you keep the barb dip low you don't lose much from not benefiting off the extra rage damage.

You can't cast spells or concentrate while raged. 

Edit: "If you are able to cast spells, you can’t cast them or concentrate on them while raging." From the Rage barbarian class feature.

Many classes are very dependent on mobility. Rogues, monks, and rangers are in trouble when restrained. Casters have a lot of problems in magical darkness or when blinded. Grappling is deadly for casters. Paladins, fighters, and barbarians are a bit easier. Just disarm them or catch them when they're not armed. For armor, coat the inside of their armor in something itchy or painful. Or drop a shiny cursed weapon on them. I'm actually curious about whether verbal components can be reasonably provided underwater or in a vacuum.

Also, a party without a wizard is going to be toast against illusions, intelligence being the single largest dump stat.