[Snake]

Those are all Main Class-only skills.

Archer - Honed Barrage
On-Critical: Your next ranged Basic Attack within 3 rounds will gain different effects, based on the weapon type and/or sub-type.

Honed Barrage (Bows): The attack will gain 3 extra "rounds", similar to a handgun, inflict Flatfoot for 2 rounds, and target all enemies in a 2-wide circle area.
Honed Barrage (Handgun/Shotgun/Rifle): The attack will inflict Flatfoot for 2 rounds, and target all enemies in a 2-wide circle area.
Honed Barrage (Launcher): The attack will target all enemies in a 2-wide circle area and have a chance (25%) to destroy tiles in the area.

After the attack is done, you will dash 2 squares in the opposite direction you are facing.

Duelist - Fleur
Exists.

Rogue - Twin Dance
Exists.

Soldier - Controlled Aggression
On-Critical: If you have a Shield equipped, gain Controlled Aggression for 2 rounds, which interacts with Guard and Bash.

Controlled Aggression (Guard): When you use Guard, increases its LV by 2 and redirect non-bonus damage (once per unit) from allies within 3 range to yourself.
Controlled Aggression (Bash): When you use Bash, perform a Shield Bash, which can inflict Knockdown if your enemy is inflicted with movement-impairing effects, and deals blunt physical damage equal to (Shield UL + Scaled DEF + Soldier LV), that ignores protection and has Great Accuracy (forces a Glancing Blow that applies effects, if the enemy evades).

Martial Artist - Hustling Blitz
On-Critical: If Weathered Body is active, and if the attacking weapon is a Fist, gain Hustling Blitz for 2 rounds after the attack.

Hustling Blitz: Enables the Riposte from Duelist base class, and Twin Dance skill from the Rogue base class, even if you do not have them active. (They will be treated as max rank.)

Bard - Battle Rhythm
On-Critical: The next song or dance skill you use within 3 rounds will cost 0M and restore 10% FP of allies within 3 range.

From this point downwards I don't think these really NEED things like it, but could be funny to have them. Opinions are welcome.

Mage - Exploit Advantage
On-Critical: Refunds all of your Offensive spell Cooldowns. (I ran out of ideas, and critical hits/basic hits don't look like a mage's thing)

Curate - Harsh Lesson
On-Critical: Lowers the cooldown of Healing spells by 1 round. (Once per round) (I ran out of ideas, and critical hits/basic hits don't look like a curate's thing)

Summoner - Raise Morale
On-Critical: All summoned Youkai have their Move increased by 3, Evoke momentum costs reduced by 1, and FP costs reduced by 75%.