I control Irelia in Battlefield 1 with Guardian Angel equipped. Opponent plays Imperial Decree and resolves. Then opponent plays Bellows Breath repeated targeting my Irelia. Does Irelia die from Bellows Breath?

Yes, your Irelia will be killed.

Because you paid the [Repeat] cost for Bellows Breath, it creates two separate instances of damage. Each instance of damage triggers Imperial Decree, placing two separate "kill" triggers on the chain.

Sequence of Events:

1. Imperial Decree is played and resolves, creating an active effect for the turn.
2. Bellows Breath (with [Repeat] paid) is played, targeting your Irelia.
3. Bellows Breath resolves:
   • The first instance deals 1 damage. Imperial Decree triggers, placing a kill trigger (ID1) on the chain.
   • The second instance (Repeat) deals 1 damage. Imperial Decree triggers again, placing a second kill trigger (ID2) on the chain.
4. The chain resolves in LIFO (Last-In, First-Out) order:
   • ID2 resolves first: It attempts to kill Irelia. Guardian Angel activates as a replacement effect, destroying itself to save Irelia. Irelia is healed, exhausted, and recalled to your base.
   • ID1 resolves next: It attempts to kill Irelia. Because Guardian Angel has already been destroyed, there is no protection remaining. Irelia is killed at your base.

Nuances:

• Replacement Effect: Guardian Angel is a one-time replacement effect. Once it is destroyed to save the unit from the first kill trigger, it cannot protect against subsequent kill effects.
• Tracking: Imperial Decree's kill trigger does not require the unit to remain at the battlefield. It tracks the unit to its new location (your base) and kills it there.
• Damage Instances: Bellows Breath with [Repeat] creates two distinct damage events, which is why Imperial Decree triggers twice.

This is my interpretation based on the mechanics of replacement effects and triggered abilities. This interaction is consistent with RiftJudge FAQ #8930 and #9419.