Batman is arguably the most popular superhero on the face of the planet, but he also has a collection of characters around him that people enjoy. They're known affectionately as the Bat-family and are comprised mostly of former sidekicks, associates, and/or people Bruce Wayne/Batman has become emotionally attached to.
In the world of Pokemon, trainers become attached to these creatures and develop lifelong bonds. By merging the two universes it'd result in Batman and company likely finding specific Pokemon they relate to and training them to fight by their side in an attempt to vanquish any and all criminal activity.
8 The Signal - Morpeko
The Signal, Duke Thomas, is likely the least known member of the Bat-family on this list. He lost his parents to the Joker, which set in motion his whole goal of becoming a vigilante despite still being a teenager. He can absorb and manipulate light as well as shadows, so a Pokemon that is either Electric or Dark-type seems like the perfect match.
It turns out that among the roster of over 900 Pokemon there is only one that is both Electric and Dark-type, and that's Morpeko. It's a small hamster with an incredible appetite and shifts between two modes, a Full Belly Mode where it's cheerful, and an anger-focused Hangry Mode.
7 Robin (Damian Wayne) - Growlithe
Damian Wayne is the son of Bruce Wayne and Talia al Ghul, meaning he inherited the best and worst traits of the two. He has an unwavering sense of determination, but that also comes with a hard-headed nature that makes him a bit stubborn at times. Being the son of Batman puts a lot of pressure on one's shoulders and Damian has always felt a need to prove himself.
Growlithe, the Fire-type canine, is a creature that passionately burns with loyalty toward those it bonds with. Once raised and evolved into an Arcanine, Damian could ride his partner into conflict, which would be a sight to behold.
6 Cassandra Cain - Umbreon
Cassandra Cain is much different personality-wise than someone like Bruce Wayne. She's rather reserved and prefers to keep her personal life quite private. It'd be safe to label her as an introvert and that provides some direction in choosing her perfect Pokemon partner.
Cats and introverts tend to work well with one another, and in the world of Pokemon, there happens to be a feline-like creature who also sports the same colors as Cain's iteration of Batgirl. Umbreon, the Moonlight Pokemon, is a Dark-type evolutionary form of Eevee. In the dark the rings on its body glow a vibrant gold, which catches most people by surprise, instilling a bit of fear in them.
5 Red Robin - Blaziken
Tim Drake might not have the stealthy charisma of Dick Grayson or the brooding intimidation of Jason Todd, but that doesn't mean he didn't grow into his own. Throughout his whole life, Drake worked twice as hard to simply earn half the respect. He's a man of passion, which easily makes pairing him with a Fire-type Pokemon the right choice.
Blaziken is a Fire and Fighting dual-type Starter Pokemon who possesses an elite physical attack and is said to become even tougher based on the strength of its opponent. It seems like combining a man known as Red Robin with a powerful bird just makes sense.
4 Batgirl (Barbara Gordon) - Espeon
Barbara Gordon is a capable and intelligent crimefighter when she takes the night as Batgirl. Her iconic purple and yellow suit fit the vibrant energy she tackles any and all problems in front of her with. Barbara fully embraces both her wit and femininity, so when looking at the roster of Pokemon, Espeon seems like a stellar pairing.
In addition to having a strong special attack and being a Psychic-type, it's said that it can read air currents with its fur which allows it to predict the movement of its enemies. Seems like a rather handy tool to have at one's side when fighting crime.
3 Alfred Pennyworth - Mr. Mime
Anyone familiar with the Pokemon anime remembers that a Mr. Mime lived with Ash Ketchum's mother and would help her with chores around the house. Alfred Pennyworth on the surface is nothing more than the Wayne Manor butler, but he acts as a morale compass and father figure for Batman from time to time and is a no-nonsense type of guy.
He'd likely want a Pokemon that carries its own weight but isn't brooding as Bruce Wayne provides enough of that for one household. Provided what it's based on, Mr. Mime is likely a much more quiet creature, which is something the older Alfred would welcome wholeheartedly.
2 Red Hood - Houndoom
Due to what he experienced at the hands of the Joker, as Jason Todd broke out on his own to serve justice from his own perspective, it seems the aspect of Batman that he personally connected with most was the fear and violence of it all. Sure, his costume looks cool, but it's also rather intimidating to anyone he steps in front of.
Having a Pokemon by his side that instills these same sorts of feelings would be crucial to Jason. Houndoom seems like the right fit as the Dark and Fire dual-type known as simply the Dark Pokemon exudes the same type of energy Red Hood provides in the heat of the moment.
1 Nightwing - Greninja
If there's one thing Dick Grayson learned from his days as Robin under Batman's wing it was that stealth was of the utmost importance. That's precisely why he would likely lean toward having a Pokemon like Greninja by his side.
Not only does it match Grayson's color scheme for his Nightwing suit, but it's a creature that would provide added value to his endeavors, instead of becoming a burden. Greninja's top base stat is its incredible speed, meaning it can keep up with Nightwing as he patrols Gotham City in search of criminals and villains.