Instructions
Set your party up with mostly mobile, ranged attackers. Additionally, make sure you have at least one strong physical character such as a Paladin or Defender who can survive a great deal of damage. Lastly, make sure you have a character who can remove negative status effects. The most effective way to add status effect removal to your team is to job change someone into a White Mage and equip them with a Pure Staff to learn Esuna. You can replay old missions if you need to train up your White Mage, but don't start the Royal Ruins mission without Esuna.
Immediately attack the Lilith with all of your troops and eliminate her as soon as possible. This enemy starts out at the left side of the map near your troops. If she attacks first, she uses an ability that inflicts a wide range of crippling status effects on one character. After being hit, her victim is completely immobilized or dead for the rest of the match without intervention from a healer. Kill her with everything you have and restore the Lilith's victim with Esuna as soon as possible.
Kill the Lamia as she approaches from the northeast corner. She inflicts the same negative status effects as the Lilith, so protect your White Mage and be ready to restore whoever she hits. At the same time, send your strong physical character to meet the Toughskin, the rock monster with the sword sticking out of its back. This beast deals heavy melee damage and takes some effort to kill.
Send your fastest ranged attackers after the two Odd Statues in the northwest corner. The statues have very few health points and do not fight back, so you can usually destroy them in one round after reaching them. Continue fighting the Toughskin with your strong physical character; the monster may disable or even kill your character, but you will be able to destroy the statues before he catches up to your fastest troops. You can largely ignore the only remaining monster, the Titania, but after the more threatening enemies are handled you can quickly take it out on the way to the statues, if you want.
Destroy the Odd Statues to win the match. With the dangerous monsters out of the way, the statues go down quickly.