This battle occurs about 51% of the way through the game (at least that's what my completion % said when I saved right before the battle) it like all but 1 achievement are story line based and can not be missed. It happens after your Investigation in Junk City and you head back into the White Flower Fields.
Earth Element monster
HP - 3600
EP - 1100
Gravity Drain - Gravity enchant that drains HP from enemy in range. Cost is 117 EP, this attack takes up 2 columns (6 blocks altogether).
Earth Strike - Strong enchant rains Earth Ether on enemy in range. PP is 446, EP cost is 135, this attack covers about half of the grid, in a 2 block (next to each other in 1 row), 2 block on opposite ends of each other (next row), and repeat.
That battle is just like all the other battles in the game, use your strongest attacks and make sure your character HP stays above 450 at all times as the Sphinx's attack does close to 450. Since you will have a golem and not 4 human characters for this fight, I recommend the Ruby Butterfly as it is an excellent healer/buffer and does the most attack damage out of the healer golems. If you would rather use Karin as your Healer, then use whatever your strongest golem is. Do not use Wind Type Golems as they will take added damage from the Sphinx's attacks and will most likely die within 1 or 2 hits.