If an opponent plays Fading Memories on my unit, can I react to the temporary trigger during my beginning phase with Tactical Retreat to save the unit?

Yes, you can react to the Temporary trigger from Fading Memories during your Beginning Phase with Tactical Retreat to save your unit.

Why this works:

1. The Trigger: The Temporary keyword on your unit triggers at the start of your Beginning Phase ("Kill it at the start of its controller's Beginning Phase"). This triggered ability is placed on the chain.
2. Reacting: Because this is a triggered ability on the chain, you have priority to play [Reaction] spells in response to it. You can cast Tactical Retreat and target the unit that is about to be killed by the Temporary effect.
3. Resolution (LIFO): The chain resolves in Last-In, First-Out (LIFO) order. Your Tactical Retreat resolves first, creating a replacement effect for that unit: "The next time it would die this turn, heal it, exhaust it, and recall it instead."
4. Replacement: When the original Temporary death trigger then resolves, it attempts to kill your unit. The Tactical Retreat replacement effect intercedes: instead of the unit dying and being sent to the trash, it is healed, exhausted, and recalled to your base.

This interpretation follows the standard interaction between triggered abilities and replacement effects as defined in the Core Rules and confirmed by RiftJudge FAQ #10278.