Pegasus uses a Toon Deck focused around the card "Toon World", a card unreleased to the public which allows him to play special Toon Monsters. Also, Pegasus plays multiple cards that allow him to take control of his opponent's monsters, which are often then turned into Toon Monsters themselves.
Specifically for his Duel with Yugi Muto, Pegasus created the cards "Relinquished", "Thousand-Eyes Restrict", "Thousand-Eyes Idol", and "Dark-Eyes Illusionist". In his first Duel with Yugi, he plays a test Deck that deals with taking control of Yugi's monsters. In Duelist Kingdom, along with his Toon cards, Pegasus' Deck mainly focused on using his opponents own monsters and card effects against them. Later on, in the anime, his Deck focused only on the Toon Archetype cards. He also uses some cards, such as "Prophecy", that allow him to take advantage of his mind reading abilities.
Please note that the cards "Doma the Angel of Silence", "Happy Lover" and "Mask of Darkness" are not used in any of his Duels but were seen when Yami Bakura held his spontaneous Tarot session with Pegasus. In the English version, Bakura explicitly states that these cards were Pegasus'. In the Japanese version, however, the Deck's owner remains ambiguous, as Bakura only refers to the Tarot Deck as "these cards". Therefore, he might have brought them himself.
In the first Scripted Duel Pegasus appeared in, he dueled alongside Bakura against Mai, Joey, and Yugi in a 3 vs. 2 duel. Singular duels were conducted, with a new duelist taking the place of his partner after his partner lost. In Pegasus' second scripted duel, he borrowed a Wind-Up Deck constructed by Billy Brake.
In Yu-Gi-Oh! World Championship 2004, Pegasus still uses a Toon Deck, modified to accommodate the rulings not present in the anime. He uses several cards which boost his Life Points, in order to balance the many Life Point payments required by his Toon Monsters (1000 for the activation of Toon World, and 500 for every attack made with a Toon). He also uses cards like Nimble Momonga and Change of Heart to gather Tributes for his many high-level monsters, as well as Cyber Jar and Morphing Jar to help him find key cards in his Deck. If he is unable to summon his Toons, he also has Black Illusion Ritual and Relinquished to turn enemy monsters' strength into his own.
As a Tier 3 opponent, Pegasus is unlocked by defeating all of the Tier 2 duelists at least five times each. The player must also have at least one copy of "Toon Mermaid", "Toon Summoned Skull", "Manga Ryu-Ran", and "Blue-Eyes Toon Dragon" in their Trunk, with none in their Deck. If Pegasus is defeated ten times, the latter restriction is removed.
↑This card is activated from the hand as a Trap Monster and Hawkin's commentary mentions it has a total of 2700 DEF after absorbing "Harpie's Pet Dragon". This may allude to Duelist Kingdom rules in which Trap Cards were freely played from the hand and how in Yu-Gi-Oh! - Episode 027 - Champion vs. Creator - Part 2, "Dragon Capture Jar" had 2700 DEF after adding "Blue-Eyes White Dragon's" 2500. However, in the anime and manga, "Dragon Capture Jar" had 100 ATK and 200 DEF. Assuming Hawkin's commentary is not wrong and all rules are followed, "Dragon Capture Jar" is used as a 300 DEF monster that can Special Summon itself from the hand in this duel.