I tried to do it with a full party. He used Giga Slash, and 3 people died. It is my understanding that Giga slash is single target.

Taken from: http://finalfantasy.wikia.com/wiki/Shadow_Lord_(boss)

Special Abilities:
Dark Nova: AoE dark magic damage
Giga Slash: Conal damage
Kick Back: Single target damage
Umbra Smash: Single target damage

Did this a couple weeks back without issue. We lost one person mostly because I was the only magic damage and ran out of mp while he was still immune to physical so whittling him down with special abilities while I rested mp drained the WHMs mana, but even dead you should get the key item so long as the rest of the party clears it.

_________________
~~Guedj~~
WAR37 MNK10 WHM38 BLM61
RDM18 THF63 PLD15 COR24
BST75 BRD46 RNG12 SAM71
NIN37 DRG60 SMN70 BLU15
DRK0 PUP0