A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
A player, 30 September 2013
Martyr reads, in the Oracle:
Reaction: After one of your Personalities is destroyed by battle resolution or by a card's effect and if the target is still in play, target a Personality in the army that opposed yours during that Resolution Segment, the card that performed the action that destroyed yours, or the card that created the effect that destroyed him: The target's controller loses 5 Honor.
What a tricky one to phrase... so if I tie a battle I can't play Martyr from my dying dudes right?
And if I use The Price of Power to kill one of my guys + one of my opponent's guys he can't use Martyr either (since the event discards itself as a cost, before the effects are applied, and then Martyr fails to meet "if the target is still in play")?
Brook Cunningham (rules official), 30 September 2013
Martyr reads, in the Oracle:
Reaction: After one of your Personalities is destroyed by battle resolution or by a card's effect and if the target is still in play, target a Personality in the army that opposed yours during that Resolution Segment, the card that performed the action that destroyed yours, or the card that created the effect that destroyed him: The target's controller loses 5 Honor.
What a tricky one to phrase... so if I tie a battle I can't play Martyr from my dying dudes right?
And if I use The Price of Power to kill one of my guys + one of my opponent's guys he can't use Martyr either (since the event discards itself as a cost, before the effects are applied, and then Martyr fails to meet "if the target is still in play")?
Both of your assertions are correct.