From the Super Mario Wiki, the Mario encyclopedia
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Paper Mario series
In the Paper Mario series, First Strikes can be used by Mario to damage or possibly defeat enemies before he takes his first turn in battle. Bosses and mid-bosses (with a few exceptions), and some enemies like M. Bushes and Hurt Plants cannot be harmed by usage of a First Strike. First Strikes can also be used against Mario; for example, if a Koopa Troopa successfully attacks Mario with its shell, Mario will get hit by the First Strike and take damage.
To perform a First Strike, Mario can simply jump on the enemy, hit them with his hammer, or hit them with an attack from a partner. Certain enemies, those being Spiky and Fire enemies will deal damage to Mario instead of being dealt damage, unless certain Badges are equipped, however this only applies to jumping First Strikes.
In Paper Mario, Goompa first mentions this to Mario as they walk through Goomba Village. First Strikes in this game can be performed by Mario, or by his partners Kooper and Bombette. First Strikes from enemies can be avoided by dodging the attack or by equipping the Chill Out badge. While the Dizzy Attack badge is equipped, Mario can inflict Dizzy on the first enemy in a formation (but does not deal damage) by using his Spin Dash move to run into an enemy before a battle. Mario can instantly defeat any enemy that would reward one or more Star Points (which is considered to be "weak"), entirely skipping the battle without rewarding Star Points, with a First Strike by equipping the First Attack badge. This property can be extended to Mario's spin dash by equipping the Spin Attack badge, and even further extended to walking by equipping the Bump Attack badge (which overwrites both First Attack and Spin Attack due to just requiring contact with the enemy in question). Mario can equip the Spike Shield badge to be able to jump on spiky enemies such as Clefts, or can equip either the Fire Shield or Ice Power badges to jump on fire enemies like Lava Bubbles.
In Paper Mario: The Thousand-Year Door, Professor Frankly first mentions First Strikes to Mario after he and Goombella defeat the three Goombas in the Rogueport Sewers. In battles, First Strikes now include Action Commands, doing more damage and possibly defeating weak enemies, such as Goombas and Dull Bones, as well as allowing him to perform Stylish Moves allowing Mario and his partners to gain Star Power before the battle fully begins. First Strikes can also be started by using Koops or Bobbery but they automatically succeed on a First Strike, removing the need to perform their respective action commands. Their Stylish Moves are still able to be performed. Flurrie can be used to stun enemies before a battle, freezing them in place making them easier First Strike targets for a few moments, however she herself cannot give enemies a First Strike. The Chill Out, First Attack, and Bump Attack badges are still available and function the same as in Paper Mario, however First Attack and Bump Attack do not work inside of the Pit of 100 Trials. With the removal of the Spin Dash, the Dizzy Attack and Spin Attack badges were removed. The Fire Shield badge was also removed, being merged fully into Ice Power.
Due to the absence of the RPG-styled battling system throughout the majority of the game, First Strikes are absent from Super Paper Mario.
In Paper Mario: Sticker Star, a First Strike has an added mechanic. By collecting HP-Up Hearts, the Hammer and jump power will increase every time when the one's digit is at a zero from five. If the power is enough to directly defeat the enemy on the course, the enemy will be defeated and will drop a coin without starting the battle. Additionally, certain enemies' field attacks directly hurt Mario, rather than triggering a battle. Similar mechanics return in Paper Mario: Color Splash, with attack power increasing with every Big Paint Star collected and enemies dropping more than one coin when defeated directly on a course with a First Strike. In Paper Mario: The Origami King, First Strikes retain their Sticker Star properties, though enemies' First Strikes are now unblockable.
Mario & Luigi series
First Strikes in the Mario & Luigi titles are similar to Paper Mario's First Strikes with one key difference – a first strike on one enemy in the field will damage all enemies in the battle. However, in Mario & Luigi: Superstar Saga and Mario & Luigi: Partners in Time, a First Strike with a hammer works differently: when Mario or Luigi in Superstar Saga, or Baby Mario or Baby Luigi in Partners in Time, hammer an enemy on the overworld, all enemies in the battle become dizzy. In later Mario & Luigi games, a First Strike with a hammer instead damages all enemies.
Bowser can also use First Strikes by punching or breathing fire (the latter of which can burn foes) on the enemy in Mario & Luigi: Bowser's Inside Story and Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey.
In Mario & Luigi: Superstar Saga + Bowser's Minions, a First Strike with a hammer can also cause enemies to begin the battle with the SPD-Down status ailment, and Hand Powers can now be used to perform First Strikes; aside from damaging enemies, Firebrand can also burn enemies and Thunderhand can also make enemies dizzy. These effects, bar the Hand Powers', return in Bowser's Inside Story + Bowser Jr.'s Journey.
As in the Paper Mario series, enemies can also perform First Strikes against one of the characters. However, if the enemy or one of its projectiles hits a character in the back, they will instead trip and will not get up until it is their turn or if they are damaged by an attack. If the front character is hit, the battle will start as normal.
Mario & Luigi: Bowser's Inside Story
Mario & Luigi: Dream Team