The fact that this is a crossover game pretty much makes the story nonsensical as there is simply no logical way to explain how all these characters from completely different universes can meet up. Based on the reactions of the characters to what's going on, though, it seems that the writers were fully aware of this and instead decided to simply have fun with it all by putting lots of innuendos, in-jokes and other references into the game. All that makes for an entertaining and amusing story that shouldn't be taken seriously.
The story aside, the game is divided into a lot of separate chapters, many of which take place in locations from the included franchises. After the beginning of the game, a base can be accessed between each chapter to check characters' stats, equipment, skills, and more. It's also a good opportunity to check out short profiles of newly-obtained characters to find out what series they're from.
Once all the preparations are complete and a chapter starts, players will usually find themselves on a battlefield filled with enemies. The tide of the battle and objectives can change several times each chapter, though. For example, enemy reinforcements might suddenly arrive. Sometimes they get to move immediately, leaving the player with no time to adjust their strategy, so it's a good idea to never play too recklessly to avoid sudden reinforcements wiping out several units. Upon defeat, a unit is disabled for the rest of the chapter until an ally moves next to them and sacrifices their turn to rescue them. Some chapters will end in an instant Game Over if certain units become incapacitated, but for the most part, death is pretty inconsequential unless the enemy manages to wipe out a majority of the small army all at once, leaving little room to recover.
The gameplay is grid-based and similar to a game like Fire Emblem: Awakening in that each unit has a certain movement and attack range, but that's where the similarities end, as the movement order is determined by a Speed stat. This means that enemies will move between player character turns and don't have their designated turn where all of them act consecutively. The first few turns are conveniently displayed on the touch screen while every unit has a corresponding number above their head, making it easy to plan ahead. Once every unit has had their turn, an overall turn will pass. Each unit can use as many items as they like during their turn and while healing items are very commonly obtained from enemies, the better ones should be saved for tricky situations.
Once an enemy is in attack range, a battle can be initiated. Two characters - that are typically from the same franchise - form a pair unit which acts as one. Each pair unit starts off with three different attacks and can gain up to five via level ups. The amount of times a pair unit can attack is based on the number of different attacks they know but an additional attack can be gained by performing each attack once. These regular attacks are performed by pressing the A button in combination with the Circle Pad. Despite its flashy looks, the combat only requires single, timely button presses and it's far from a fighting or an action game. Most attacks will lift the enemy into the air, making them susceptible to even more punishment. Fighting with just one pair unit isn't desirable, though. Each pair unit can have a separate solo unit accompany them. They can be called in once during each battle along with an ally that's standing next to the attacking unit. Timing is key, here, as the Solo and Support Attacks combined with the first units' attacks create Cross Hits. These freeze an enemy in place and are ideal to dish out a lot of damage. This is particularly useful for enemies that can block attacks, as it disables them from recovering after the initial guard break.
Each battle grants a certain amount of experience that's boosted by the highest combo of dealt Hits, Cross Hits and Critical Hits. Critical Hits are performed by attacking exactly before the enemy touches the ground after being launched into the air. Some regular attacks are very easy to get Critical Hits on, while others are a bit trickier. Thankfully, the included Training Mode allows the player to conveniently practise the timings for each particular attack and the boosted experience as well as the increased damage makes it worth that extra effort. Not to be confused with regular experience are XP - also known as Cross Points - that are accumulated by successfully attacking enemies. XP are used for activating certain skills outside of a battle as well as performing Special Attacks in combat. These Special Attacks are incredibly powerful and it's possible to perform Critical Hits with them, too, making them even deadlier. They are also a joy to watch, with special music based on the franchise kicking in while the characters obliterate the enemy in the most stylish and over the top way possible. One would think that the spectacle would wear off eventually, but even after hours and hours of playing the game, watching these Special Attacks is still entertaining, even more so with a Critical Hit.
Skills and Special Attacks aren't everything XP are used for, though. When an enemy attacks, the player has to pick a response. Defend halves the damage received, Full Defend completely nullifies the attack, while Counter allows for a short counterattack. All of these actions cost certain amounts of XP. The regular maximum is 100% and beyond that it can only be increased by performing Cross Hits with Solo or Support Attacks. XP will also diminish over time if they aren't used, so it's important to use them up fairly quickly. Bosses have their own special meter that increases as they take damage, meaning a boss can quickly dish out a lot of damage to multiple surrounding characters in return. Speaking of which, Multi Attacks can be learned by allies, as well, and are very handy when it comes to quickly dispatching a lot of grunts that are stationed next to each other. Much like Special Attacks, they also use up XP.
Each pair unit can also equip a weapon and an accessory. These can be found in treasure chests on the battlefield or obtained by defeating bosses. Most of them don't provide significant improvements on their own, but combined with the ability to assign a Solo Unit with specific abilities to a pair unit, it gives players the option to customise their units to a certain extent. The right combinations can make a difference but it's not critical as the game is already relatively easy.