Blood For Blood

Blood For Blood is a Crucible medal triumph: defeat an opponent who just defeated an ally. Samurai Gamers describes the medal as killing an enemy player who just killed one of your allies.

How to complete

Stay close to teammates and trade: when an ally dies, immediately kill their killer (use the Radar and teammate callouts). Playing in a group and pushing together makes revenge kills far more frequent.

The required medal count and whether non-Crucible modes award it are not confirmed by the page I opened.