"Andro Sphinx" and "Sphinx Teleia".
The first group consists of LIGHT-Attribute, Beast-Type monsters. These are "Andro Sphinx", "Sphinx Teleia" and "Theinen the Great Sphinx". They were released in an exclusive pack after the release of Yu-Gi-Oh! The Movie: Pyramid of Light.
"Pyramid of Light" quickly Summons the former two at a cost of 500 Life Points each, creating strong beat-sticks for no tribute (they can't attack the turn they are summoned though). These monsters cannot be Special Summoned from the Graveyard, so you will need to stop them from getting destroyed by your opponent's card effect (most preferably by using the effect of "Stardust Dragon"). Or, if they are destroyed, return them to your hand using "Monster Reincarnation".
The reliance that these monsters have on "Pyramid of Light" can also be a disadvantage for two reasons: they are Dead Draws in case you don't get, and it can be easily destroyed, specially with cards like "Nobleman of Extermination", which can remove all three copies from play at once. However, even if cards like "Jinzo" or "Royal Decree" negate "Pyramid of Light", "Andro Sphinx" and "Sphinx Teleia" can still be Special Summoned because they do so through their own effects.
"Theinen", the Triumph card, can be Summoned only by paying 500 Life Points when "Andro" and "Teleia" are removed from the field at the same time, making him a life saver in case your opponent destroys your monsters with Dark Hole or destroys the "Pyramid of Light" (which destroys both of them). One big problem with "Theinen" is that even with his one time boost, his attack is not enough to OTK the opponent (6500, 1500 points short). Also, he is one big Dead Draw in a Deck that already has problems with drawings.
They mainly enhance Deck which use the "Once per turn, you can flip this card into face-down Defense Position" effect. Though it has to be Tribute Summoned, "Hieracosphinx" prevents your face-down monsters from being attacked. "Criosphinx" forces your opponent to discard card(s) from his/her hand after the same number of monster(s) on his/her side of the field return to his/her hand. Therefore "Criosphinx" and "Guardian Sphinx" form a combination which can prevent your opponent from viably Summoning anything.
"Exxod" is not a "Sphinx", but can only be Special Summoned by Tributing a "Sphinx". "Exxod"combined with "Hierarcosphinx" makes a lethal force; every time an earth monster is Flip Summoned, "Exxod" inflicts 1000 points of direct damage to your opponents Life Points. With "Hierarcosphinx" on the field, your face-down cards cannot be attacked. The cards except "Hieracosphinx" are especially vulnerable to "Gaap the Divine Soldier" and "Final Attack Orders".
Also, "Dark Simorgh" and "Light of Intervention" can kill the effects of "Guardian Sphinx" and "Exxod, Master of the Guard" because a player will be unable to Set their monsters face-down, therefore monsters cannot be Flip Summoned.
"Clear World" is also a good addition to this Deck, since cards in this Deck have the effect of being flipped face down, and face down cards cannot be targeted by "Clear World".