After speaking with the Sphinx, follow the marker on your minimap to the entrance of the Manticore Lair. It shouldn't be too hard to get from where you currently stand to the entrance, although levels are randomly generated to an extent so we can't say for sure.
The Manticore's Lair is a simple one floor dungeon, although it has a minimum level requirement that you must meet before you can enter it. Of course, if you're not of this level already you probably have no business being anywhere near the lair in the first place, as this is just the minimum requirement and if you've been doing side quests and seeking out all of the treasure and named creatures in an area you are probably high enough to get in there and wreck some monsters.
If for whatever reason you aren't at a high enough level to get into the dungeon, return to the desert and grind some levels or, better yet, seek out any side missions that you may have missed and complete them. This is a great way to get extra loot, too.
When you are ready, step into the Manticore's Lair. Many of the enemies here use Poison weapons, so you will want to equip Poison resistant gear if you have any. You should also be aware that, unlike in the last dungeon you faced, the Manticore's Lair plays host to a number of long-range enemies who will take potshots at you from a great distance. In order to best face this dungeon, you will want to actually run past the close range melee enemies to deal with the archers first. Then, when you are no longer being attacked from a distance, you can return to the melee fighters and finish them off.
Melee attackers, like before, will be heavily armored but largely pretty slow. You can get around them pretty easily, so pick off the fastest enemies first and the slower enemies later. You will soon develop a pattern of going into a room, picking off the ranged enemies first, dealing with the faster of the melee attackers second, and then finishing off the big hulking brutes third.
It won't be long before you reach the lair of the Manticore. As usual, when you find his lair you should pop a health and mana potion or two, whatever it takes to let everything refill. If you have gear that regenerates your resources, wait for them to regenerate instead of wasting potions. Also, buff your pet before entering the boss room. Enter the lair when you are ready.
The Manticore is a powerful enemy with high health and defense, and he has attacks that deal damage to a fairly large area of the battlefield. His whirlwind attack in particular can be pretty nasty. It's difficult to avoid, so try simply getting in close and hitting as quickly and for as much damage as possible. Always be sure to keep your health very high, because the Manticore has a little trick up his sleeve (paw?)
As it turns out, there's a second Manticore in the lair. The Manticore's Mate will appear partway through the battle, and it'll be just as tough as the first one. Ignore the Mate for now and continue to attack the original Manticore. The sooner you can finish off the first one, the sooner you can truly focus on finishing off the second one and ending the battle for once and for all. As always, keep a careful eye on your health and mana, and spam your skills to inspire status effects and deal big damage to the bosses.
Once both of the Manticores have fallen, search through their lair. There will be lots of gold to find throughout the lower area of this lair. Pick up all of the gold before looting the giant chest for the best treasure of all. Once you have looted the area and finished off all of the enemies, leave the Manticore's Lair and return to the Sphinx with the good news. You will receive your reward for this quest and get the next phase of the story unlocked for you.