If my unit dies in Showdown during opponent's turn, can I return it if I hold Altar of Blood?

Yes — if your unit is at Altar of Blood and it would die during combat (including lethal combat damage during the Combat Cleanup), you can pay [A][A][A] to heal it, exhaust it, and recall it to your base instead. This works on your opponent's turn; you just need the power available in your rune pool.

Two things to note:

• You don't need to Hold/control Altar of Blood — the replacement applies to any unit at that battlefield, so it works even if your opponent controls it and your unit is attacking there.
• It only replaces deaths "during combat." A kill during a Non-Combat Showdown (conquering an empty battlefield) wouldn't be covered. If multiple units die at once, the turn player decides first whether to pay, then the other player in turn order (Rule 373.1; FAQ #11503).