Badges In Destiny 2 Crucible

There is a list of the badges and what they mean in game which is under Crucible in the Triumphs screen.

Here is a list of them collected by the playing community:

• Best Served Cold - Killed an enemy player who killed you
• Blood for Blood - Killed an enemy player who just killed one of your allies
• Cold Fusion - Go on a Fusion rifle spree.
• Combined Fire - Kill an enemy player by shooting at them as a team.
• Counter Attack - Get a kill while being the last guardian standing.
• Crushed Them - Win a match with a large margin of victory.
• Barricade Breaker - Killed an enemy Titan and destroy their barricade.
• Dodge This - Killed an enemy Hunter during their dodge animation.
• Rift Breaker - Killed an enemy Warlock during their rift phase.
• Dominant Advantage - Score five Advantage or Power Play kills before the opponent recaptures a zone.
• Pitch Perfect - Defeat an opponent with Hammer of Sol at a distance greater than 30 meters.
• Everything Looks Like a Nail - Defeat three opponents within a single Hammer of Sol activation.
• Regent - Killed two enemy Guardians with a sword.
• Annihilation - Land final blows on the entire enemy team before any of them respawn.
• Double Play - Kill 2 enemy players in rapid succession.
• Triple Play - Kill 3 enemy players in rapid succession.
• Lights Out - Kill 4 enemy players in rapid succession.
• We Ran Out of Medals - In a single life, defeat 20 opposing Guardians.
• Fight Me! - Deal the most damage in a match.
• Flag Bearer - Secure the most capture zones during the match
• Reclaimer - Recapture a zone within 15 seconds of it being captured by your opponents.
• Gangs All Here - All allies must survive at the end of a Countdown round.
• Hawkeye - In a single life, defeat two opponents with precision Hand Cannon final blows.
• Hurricane - Kill three enemy Guardians in a single Arcstaff super activation.
• I Live Here Now - Hold two or more zones for at least 1 minute.
• Lethal Instinct - Defeat an opponent within 2 seconds of activating Golden Gun.
• Lightning Strike - Defeat an opponent within 3 seconds of activating Arc Staff.
• Never In Doubt - Win a match in which your team never trailed.
• Handful of Bullets - Kill three enemy Guardians in a single Golden Gun super.
• Not So Fast, My Friend - Defeat an opposing Guardian using your Super while their Super is active.
• Direct Hit - Kill an enemy player instantly with one shot from a Grenade Launcher.
• Power Overwhelming - As a team, defeat all 4 opposing Guardians at least once during a single Power Play.
• Quick Strike - Get the first kill in a game (to be confirmed).
• Ruthless - Perform a 5-kill streak.
• Unyielding - Perform a 10-kill streak.
• Shutdown - Kill an enemy player who is on a kill streak.
• Splash Damage - Kill 2 or more enemy players with a Rocket Launcher.
• The Cycle - In a single match, land at least one final blow with each class of weapon (Kinetic, Energy, Power) and ability (Melee, Grenade, Super).
• Wrecking Crew - As a team, defeat 7 opposing Guardians without any of your team dying.
• Lethal Cadence - In a single match, defeat 7 opponents with Pulse Rifle final blows.
• Undertaker - Land all knockout blows on the opposing team in a single round.
• Time and a Half - Win a match in overtime.
• Undefeated - Complete a match in which you are never defeated by an opponent.
• Sub machinist - In a single life, defeat 2 opponents with Submachine Gun final blows.
• One for Each of You - In a single life, defeat two opponents with precision Hand Cannon final blows.
• Field Scout - In a single match, defeat 5 opponents at long range with Scout Rifle final blows.
• Striker Special - In a single activation, defeat two opponents with Shoulder Charge, then a third with Fists of Havoc.
• Absolute Force - Defeat two or more opponents in a single Fists of Havoc slam.
• Flying Fortress - Defeat an opponent with a Shield Rush within 3 seconds of defeating an opponent with a Sentinel Shield melee.
• Perfect Guard - Block fatal damage within 2 seconds of activating Ward of Dawn.
• Longbow - Defeat an opponent with Shadowshot at a distance greater than 30 meters.
• Falling Star - Defeat an opponent with Brimstone while Daybreak is active.
• Defying Gravity - In a single Daybreak activation, defeat two or more opponents without touching the ground.
• Singularity - Defeat an opponent with a Nova Bomb Vortex.
• From Downtown - Defeat two or more opponents with a Nova Bomb that was in the air for at least 5 seconds.
• Thunderstruck - Defeat an opponent with Landfall while casting Stormtrance.
• Lightning Storm - Defeat two or more opponents in a single Stormtrance activation.
• Entangled - Defeat a tethered opponent within 5 seconds of casting Shadowshot.

Thanks to Timmy Jim for the link to the Destiny 2 Wiki

Reference to medal details from the game's API.