The Stealth Soldier is a special Heartless introduced in Kingdom Hearts Final Mix. As it's name implies, it's a tougher version of the Soldier Heartless and drops the rare Energy Stone synthesis item.
Finding the Stealth Soldier
The Stealth Soldier Heartless are found in the Grand Hall and Entrance Hall in Hollow Bastion. You will know when a Stealth Soldier will appear in the Entrance Hall when a single Large Body and two Wizards spawn near the fountain; in the Grand Hall, they'll appear along with two Large Body Heartless during the second wave in the foyer, and after defeating three Large Body Heartless near the the entrance to the Dark Depths.
Prior to completing the first story episode in Hollow Bastion, one Stealth Soldier appears alongside four Darkballs in front of the fountain; one other Stealth Soldier appears alongside a Defender and two wizards behind the fountain on the upper level, near the Heartless sigil door. Stealth Soldiers will not appear on the second floor balcony until after completing the first story episode here.
Defeating the Stealth Soldier
The Stealth Soldier is super-fast and super-powerful! The Stealth Soldier will be invisible when it spawns; use your lock-on to locate them quickly. Cast Stopga magic to briefly halt them and make them appear, then strike with as many combos as you can. When you deal enough damage to them, their invisibility will be disabled. Continue to cast Stopga and follow up with combos.
If the Stealth Soldier is the final Heartless remaining from the group of Heartless it spawned with, it will disappear immediately. You'll need to keep one other Heartless alive while you focus your attacks on the Stealth Soldier(s).
Obtaining the Energy Stone
If your goal is to obtain Energy Stones, you'll want to defeat them as quickly as possible. It's highly recommended for the party to be level 65 or higher, equip all Lucky Strike abilities to the party, and use a keychain that boosts magic like Oathkeeper or Diamond Dust. The Energy Stones have a default drop rate of 35%.
If you're trying to get the Stealth Soldiers to respawn, try leaving the world via gummi ship and immediately returning.