True Shadow says "Deplete this card while defending to apply +1 dodge to the defense results."

Since RRG p.9 says under Conflicts "While attacking, mission rules are resolved first, followed by effects from the attacker (including figures friendly to him), then effects from the defender (including figures friendly to him)." I guess I can wait to use my abbility after my opponent uses abbilities like the one on Spread Barrel that gives one damage result. But I do have to use my abbility before my opponent uses surge abbilities to gain damage icons.

Right?

Yes. True Shadow is adding or removing symbols or accuracy, so it must be used during step 4. Apply Modifiers (defender).

· Any ability that is resolved "while attacking" or "while defending" can be used at any point during the attack with the following exceptions:
-- An ability that adds dice to a dice pool can only be used immediately before step 2 of the attack.
-- An ability that allows a player to reroll dice can only be used during step 3 of the attack.
-- An ability that allows a player to modify die results can only be used during step 4 of the attack.

Further reading with more information:

https://www.boardgamegeek.com/thread/1631857/ability-resolution-order-during-attacks

Quick follow up question;

What about abilities that add or remove keywords. Like Power to Shields?

I assume it's latest use can be in step 4: Apply Modifiers, although the RRG doesn't mention removing/adding keywords in that step, or at all...

I guess keywords are modifiers? Although RRG only mentions icons or accuracy?

Keywords are not symbols or accuracy. Pierce is taken into account during step 7 of the attack - confirmed by a ruling from FFG (it does not cancel or remove blocks, it is just taken into account when calculating damage as per the RRG). Blast and Cleave and condition keywords are resolved after the attack resolves, after step 7 of the attack.

So, Power to Shields can be used anytime before step 7 for removing Pierce and anytime during step 7 for other of the listed keywords.

ah, So the Imperial can wait until after surges have been fully spent in step 5, accuracy has been checked in step 6 and then even to see what the damage totals are going to be in step 7 before triggering Power to Shields?

Follow up question: The rules for depleted say I can't use the depleted card for the remainder of the mission. But what if the character/group with the depleted attachment is defeated? Would I get it back to my hand and could use it on another deployment?

You can get a depleted card back, but because it is depleted, it stays face down until the end of the mission, and you thus cannot attach it to any group (without its text it isn't an attachment anymore).