Can I use Challenge and a Unyielding Spirit to both kill an enemy unit and keep mine?

No, you cannot use Unyielding Spirit to prevent damage from Challenge.

According to multiple RiftJudge FAQs (e.g., FAQ #1124, #8394, #2890), Unyielding Spirit only prevents spell or ability damage. Challenge does not deal damage itself; rather, it instructs two units to deal their Might as damage to each other. Because this damage is dealt by the units—not by the spell—it bypasses the protection provided by Unyielding Spirit.

Interaction Breakdown:

1. Challenge: When you play Challenge, it creates a chain. You choose one friendly unit and one enemy unit.
2. Damage: When Challenge resolves, the two units deal damage to each other based on their Might. This damage is "combat-like" and originates from the units, not the spell.
3. Unyielding Spirit: If you play Unyielding Spirit in response (or beforehand), it will not prevent this damage because it is not spell or ability damage.

As a result, your unit will still take damage from the enemy unit during the resolution of the Challenge, and the enemy unit will take damage from your unit. Unyielding Spirit will not protect your unit from this damage.