If I use Mirror Image to create a copy of a unit, and I decide to use the copied unit as the sacrifice for the additional cost to summon Atakhan, which energy cost does Atakhan check for?

Atakhan checks the Reflection token's copied cost — the printed Energy and Power cost of the unit it copied — not the token's own (nonexistent) cost.

So if your Reflection copied a unit that costs, say, 4 Energy and 2 Power, killing it makes Atakhan cost 4 less Energy and 2 less of its Power pips. Rule 206: effects that determine a card's cost always use its printed or copied cost — and the example there explicitly covers this exact interaction (a Reflection copying Noxus Hopeful gives Atakhan −4). A Reflection that hasn't copied anything, or that copied and failed (target left play), stays a 0-cost token and gives no reduction.

The copy only carries the unit's printed characteristics, not buffs/gear — but cost is a printed trait, so it's included.