A Climax move is essentially a super move, to put it in the simplest form possible. They come in three forms - a Climax Mode, Attack and Finisher, all tailoured to the character of choice. However, they can't always be executed on command - to use a Climax move, the player must first build up Chaos energy by engaging in fights, dealing, recieving and defending against damage, taunting enemies or in some cases just generally driving them nuts. The Chaos energy your character has is denoted by a meter divided into three segments - once a segment has been filled, your character can use a Climax move in exchange for it
The Climax Mode for a character puts them in an alternate state that lasts for a varying amount of time. Whilst in this state, they recieve benefits unique to the character, such as flight, enhanced comboability and/or damage and flinch removal, among many other examples. These are generally the more versatile of the character's moves and can be used to deliver pain in a manner most fitting to the player and the situation, making them less predictable and counterable than traditional super moves.
The Climax Attack IS the traditional super move, for the most part. When activated, the character will perform a scripted attack or series of attacks in sequence before returning control to the player again. While most of them are melee-based moves, some are executed as projectile attacks that are aimed at the player's cursor when triggered. The key advantage of the Climax Attack, besides the sheer damage they're typically capable of, is that they're one of relatively few moves that can be activated completely independant of context, which bypasses the need for contextual mindgames and get straight to the hurt. All characters have two of these with different purposes between them.
The Climax Finisher is a lot like a Climax Attack, only it's more difficult to execute, does MUCH more damage, and is accompanied by an ingame cinematic when a character successfully unleashes one. It also gains Chaos energy seperately to Modes and Attacks, and even when the player uses one of the former, the Finisher retains its own charge overlayed on top of the other Climax moves even when a Climax is executed. On the flip side, the player needs to fill all three bars with Finisher energy to be able to execute it, usually not making it available until the later stages of a fight.
In some areas of the game, most notably the majority of Single Player and in some options of multiplayer-based gametypes, you will be given more than one character to use at any given time. While they don't fight simultaneously alongside the player most of the time. they can be called into action at any time to assist the player in various ways, keeping the gameplay still based on a single character whilst offering ways for others to be useful in the meantime.
The first facet of Multi-Char gameplay is simply switching between characters. When the assist button is held down, your current character jumps offscreen and leaves gameplay, followed shortly by the next character of choice entering the field to continue in their place. Characters function seperately in this regard because they all enter gameplay in completely different ways when called for a character switch - for example, Psi is initially invisible when switched in and enters the field from behind the targetted enemy, whereas Techron falls from the sky more or less directly above the target. While these switches can make for some unexpected and useful vantage points to catch the enemy off guard, it's important to note you can be vulnerable immediately after a character switch, and an enemy can punish a switch easily if you prove to be too predictable or inappropriate about it.
More importantly, though, is the straight-up character assist. When the assist button is tapped instead of held, the secondary character will appear alongside your character, execute an attack or series of attacks appropriate to the immediate situation, then leave again and let the player get back to business. Assists can be triggered completely independant of any context the player is currently experiencing - while they can be used to make up for the shortcomings of your current character, not only can they be called in to extend combos in a well-planned brutal duet, they can even be called into on cue to interrupt an enemy's combo in progress. However, even though the characters aren't in full control of the player, they are still in effect playable characters - they still have their own health bar, and can still be attacked by enemies if given the chance, so sometimes care must be taken to ensure they aren't called in during a risky situation.
To prevent abusing assist benefits by way of spamming, there is a brief cooldown between assist usages - a few seconds for a temp assist, slightly longer for an outright character switch. While the delay is enough to prevent someone rapid-firing assists constantly to effectively give them the immediate power of two characters instead of 1.5, it's not nearly intrusive enough to be considered an issue as far as triggering it whenever it's explicitly needed.