Bayonetta slows down time, then attacks her opponent.
Witch Time is a major mechanic in Bayonetta, where Bayonetta/Jeanne slows down time while moving freely within it. It is used to traverse terrain that would otherwise be inaccessible, such as water or rock fragments. It can be activated in a variety of ways, primarily by dodging enemy attacks at the right time, as well as being activated by various accessories. Lumen Sages possess a similar ability called Light Speed, which also lets them slow down time. Various other releases by PlatinumGames and its predecessor, the Capcom subsidiary Clover Studios, also feature slowdown powers, such as the Bangle of Time in Devil May Cry, the "Slow" VFX ability in Viewtiful Joe, Veil of Mist in Okami, "Focus" in Transformers: Devastation, "Blade Mode" in Metal Gear Rising: Revengeance, and both Unite Bomb and Hero Time in The Wonderful 101.
Bat Within is a technique purchasable from the Gates of Hell. By dodging at the last second, Bayonetta instead activates Bat Within, transforming her into a swarm of bats to escape, while also negating the damage taken from the attack and slowing down time for an extended duration, unlike in Smash.
The way Bat Within works in SSB4 during Witch Time is the opposite to how it works in Bayonetta; it instead activates as Witch Time ends, and reduces slowdown time if both are activated instead of increasing it. Interestingly, Bat Within triggers in the first four frames of her air dodge and sidestep, and from the 3rd to 5th frame of her roll, which is more in line with the technique's original intended use, though in every case, it only halves the damage she would have taken, rather than completely negating it.
Bayonetta performs a backflip, and if struck at frame 5 or later, activates Witch Time, which slows down nearby opponents (including any who did not attack) dramatically for up to four seconds, leaving them open to a counterattack. This slowdown effect triggers on any enemy that hits Bayonetta with a non-projectile move; it can be activated by projectiles, but it will not slow down the user if they are too far away. Its effect is greater than that of the Timer item, slowing opponents down to 1/8 speed. This is accompanied with the visual effect of a purple vortex and a clock surrounding the victim. The slowdown duration is signified by the clock's hand, and upon making a full revolution, the effect wears off. If Bayonetta flinches during the effects, it wears off immediately.
The duration of the slowdown varies based on the victim's damage percentage and how frequently the move is used (which can reduce the slowdown time to as low as only half a second, as of version 1.1.5), regardless of whether it's successful or not. This makes it the only counter where the opponent's damage is taken as a factor and also where the strength or damage of the opponent's move is not taken into account, meaning that even weak attacks can be infamously punished. The move will fully recharge after 21 seconds without use. Though the hit used to activate will be nullified, any other hitboxes produced by the affected character will still be considered active under Witch Time, meaning that multi-hitting attacks can still potentially flinch Bayonetta and stop the slowdown if she is not quick enough to intercept. This can notoriously cause a KO on Bayonetta when she would have had the upper hand, such as against Charizard's Flare Blitz, since it can still land with full power if she walks into Charizard. Also, there is high ending lag (21 frames) which allows Bayonetta to easily get punished if an attack doesn't connect.
Witch Time does not work against grabs, though attempting the move gives the user intangibility frames which will make grabs miss, just like Lucario's Double Team. Furthermore, unlike all other counters, it can activate on non-grab unblockable attacks. It can also affect opponents while they are invincible, but not when they are completely intangible. Bosses and enemies can be affected by the move as well, but with the exception of the Master Shadow form of Master Core, they will not display the clock visual effect.
If Witch Time's effect is activated right before the counter frames run out, Bat Within activates instead: Bayonetta will transform into a swarm of bats and travel in any direction the player wishes, while halving the amount of damage taken. This mechanic technically gives Bayonetta the least vulnerable counter. It also makes it the only counter that has a safety net if activated too late, which allows easy punishes. It is also possible to activate both Witch Time and Bat Within at the same time, since the activation times for the two moves overlap within 5 frames of each other. When they are both activated, the slowdown time is reduced to 2/3 of the usual slowdown time, and Bayonetta will take the halved damage.
When attacking a slowed-down opponent with a charged smash attack, the damage increase from charging them is halved, dealing only 20% more damage when fully charged instead of the usual 40%.  This is most easily seen with the late hit of her up smash, which normally does 15% damage uncharged, but will only deal 18% damage fully charged on a slowed down opponent; otherwise, it would deal 21% damage.
Witch Time begins at a base duration of 180 frames, but increases by 1 frame for every 10% damage the opponent has, up to a maximum of 240 frames. Each use decreases the duration by 75 frames, down to a minimum duration of 30 frames (2 continuous uses). This floor is applied before the damage modifier, meaning a 600% opponent will be slowed down for 30 + 60 or 90 frames. Its duration recharges by 0.06 frames for every frame it is not used; thus, it takes 1250 frames or ~20.8 seconds to recharge from one use of Witch Time.
The values for Witch Time in Smash Ultimate can be found here.
Special Move customization was added in Super Smash Bros. 4. These are the variations:
Like the other DLC characters, Bayonetta lacks custom move variations.