This isn't really "Synchron Prediction Princess", but I really don't know what else to call it. This Deck utilizes an engine that I like to call the World Legacy engine which is a 1-card combo that gets you to World Legacy Monstrosity while also setting you up for a good position to go into a Level 9 Synchro monster to turn on said Monstrosity. I would be calling it the "Knightmare engine" but since Knightmare Mermaid is banned, we can't really call it that, as with Mermaid, it is a 1-card combo to both Monstrosity and a Level 9 on field in Knightmare Incarnation Idlee which you get from Deck with Mermaid. I always knew that this engine was a thing but I really never experimented with it much because I just felt like not even attempting to do anything with it while Mermaid is banned. So, Girsu, the Orcust Mekk-Knight serves as a 1-card combo to get you to World Legacy Monstrosity and also gives you adequate set-up to go into a Level 9 Synchro monster to have a target on field for the Monstrosity you searched for. Normal Summon Girsu and activate its effect on Summon to send an Orcust or World Legacy card from Deck to GY. Send a copy of World Legacy - "World Armor" from your Deck to the GY. Since you control no other monsters, you can Special Summon a World Legacy Token to both player's field in Defense. Link off Girsu and the Token to go into Lib the World Key Blademaster which we are able to do because we have a World Legacy card in GY. And because a World Legacy monster is in GY, we can activate Lib's effect to set a World Legacy Spell/Trap from Deck which you are using to get a copy of World Legacy Succession. If you get World Legacy Monstrosity with this effect, you are not able to actually activate it, even if you already have a World Legacy monster in GY which you do, because it's a Quick-Play Spell, meaning that it cannot be activated the turn it is set. With our set copy of Succession, we Special Summon back World Armor to a Zone Lib points to. World Armor on Special Summon searches for a World Legacy card from Deck, getting you Monstrosity. Now, if Knightmare Mermaid were legal, we would Link off Lib and World Armor into Knightmare Cerberus or Knightmare Phoenix, Link whatever we Summon into Knightmare Mermaid, discard a card and Special Summon Knightmare Incarnation Idlee to our field from Deck. But that isn't possible, so what we can do after getting Monstrosity off of World Armor is Special Summon Assault Synchron from hand and Synchro it with World Armor into a Synchro 9 for a target on field for Monstrosity. So what are we playing the Synchron cards for? Other than Assault Synchron who we are using to Synchro into a Synchro 9, we are using Junk Converter to either search for Assault Synchron for the aformentioned reasons or to search Junk Synchron in order to Normal Summon and bring back said Converter to go into Accel Synchron. Just like Denglong, First of the Yang Zing, Accel Synchron can send a monster from Deck to GY to modify its Level. While Denglong sends a Wyrm from Deck to GY to copy its Level, Accel Synchron sends a Synchron monster from Deck to GY to either increase or decrease its Level by the Level of the sent monster. We are sending the Level 4 Stardust Synchron (because IDK why you would choose to play Hyper Synchron, Road Synchron, or Bri Synchron) in order to increase Accel Synchron's Level by 4, making it a Level 9, meaning that it can now be targeted with Monstrosity. Another benefit of playing the Synchron stuff is because it gives you a good Small World bridge to either Girsu or Assault Synchron. There's nothing really special about this Deck other than being able to actually search for Monstrosity easily and consistently, but I guess you could compare it somewhat to Ham Prediction Princess. However, while this Deck gives you good Monstrosity access, if you are unable to access Girsu or Prediction Princess plays, you really have nothing to work with as opposed to what you can do in Ham Prediction Princess.
For the monsters: We are playing 3 Prediction Princess Tarotreith, 1 Prediction Princess Tarotrei, and 3 Prediction Princess Bibliomuse. Tarotreith must be either Ritual Summoned or Special Summoned by Tarotrei's End Phase effect. Her Flip Effect allows you to Special Summon a Flip Monster from Deck face-down and she can Quick Effect flip any number of your monsters face-up or face-down. Tarotrei can Quick Effect flip a monster face-up or face-down and can Special Summon a Flip Monster from hand or GY face-down during the End Phase. Bibliomuse can Special Summon herself back from the GY if she is tribtued and sent there. Her Flip Effect adds you a Prediction Princess other than herself and a Ritual Spell from Deck and while face-up on field, she gives your Ritual Monsters targeting and destruction protection from your opponent's effects. 2 Deus-X Krawler which negates all activated monster effects on your opponent's side of the field after it has been flipped face-up. And if it is destroyed on field, you can add a Level 9 monster from Deck with a different Type and Attribute than it. 1 World Legacy - "World Armor" which can Special Summon itself from hand when a monster is Flip Summoned. You are usually never going to be able to do this because when you flip a monster using an effect like Tarotrei's or Tarotreith's, that is not a Flip Summon, meaning that World Armor does not trigger. So, you are usually only going to be Special Summoning it with Lib setting Succession like I explained earlier. On Normal or Special Summon, it can add a World Legacy card from Deck to hand which is always going to be World Legacy Succession. It's last effect is not relevant as we are never going to be Normal Summoning or Setting this card. 3 Girsu, the Orcust Mekk-Knight which dumps an Orcust or World Legacy card from Deck on Normal Summon and if you control 2 or more other cards its column, you can treat it as a Tuner this turn. All you need to worry about this effect is dumping World Armor from Deck with it. If you control no other monsters, Girsu can also Special Summon a World Legacy Token to both fields in Defense. 1 Stardust Synchron which we need to send off of Accel Synchron to modulate its Level. Accel Synchron can only send from Deck which means that we need to keep Stardust Synchron in Deck if we are going through with that line. 3 Junk Synchron which Special Summons back a Level 2 or lower monster from GY in Defense with its effects negated on Normal Summon. 3 Junk Converter which sends itself and a Tuner from hand to GY to search for a Synchron monster. You are either getting Junk Synchron or Assault Synchron with this. And it is sent to GY as Synchro Material, you can target a Tuner in GY and Special Summon it in Defense but you cannot activate its effects this turn. If anything the monster you Summon back is extra Link Material to go into I:P alongside the Aggregator you possibly make. 2 Assault Synchron which you can Special Summon from hand and take 700 damage and it also Synchro locks you while its on the field this way. This along with World Armor turns into a Synchro 9 for Monstrosity.
For Spell/Traps: 3 Underworld Ritual of Prediction which Ritual Summons a Prediction Princess Ritual Monster from hand or GY face-up or face-down and you can banish it from GY to Special Summon a non-Ritual Prediction Princess monster from Deck face-down. 2 Tuning which adds a Synchron Tuner from Deck and then sends the top card of the Deck to the GY. This basically acts as your extra copies of Assault Synchron or even Junk Synchron if necessary. 2 World Legacy Monstrosity which can either Special Summon a Level 9 from hand or target a Level 9 you control and Special Summon 2 Level 9's from Deck with a different Type and Attribute than it with different names. 1 World Legacy Succession to be set off of Lib which Special Summons a monster from GY to a zone a Link Monster points to. 3 Small World. 1 Instant Fusion for Master of Ham. 3 Pot of Prosperity and 3 Infinite Impermanence.
Extra Deck: 1 Master of Ham. 1 Psychic End Punisher as we can make it with Assault Synchron and a Level 9. 1 Cloudcastle and 1 Ravenous Crocodragon Archethys which are our Synchro 9's. Cloudcastle on Synchro Summon brings back a Level 9 from GY and Crocodragon draws a card. 1 Accel Synchron which can send a Synchron monster from Deck to GY to increase or decrease its Level by the Level of the sent monster. 2 Herald of the Arc Light which searches for a Ritual Monster or Ritual Spell if sent to GY. 2 Mereologic Aggregator, 1 Laevateinn, Generaider Boss of Shadows, and 1 Jormungandr, Generaider Boss of Eternity. 1 S:P Little Knight which we can Link off Aggregator and Lib to go into. It's not as good as using I:P to go into it on your opponent's turn, but it is still interruption and a generic Link. 1 I:P Masquerena. 1 Lib the World Key Blademaster which can only be made while you have a World Legacy card in GY. During your Main Phase, you can set a World Legacy Spell/Trap from Deck but it cannot be activated unless you have a World Legacy monster in GY, and if it is sent to the GY as Link Material, you can shuffle a card on field into the Deck, including the World Legacy Token you gave your opponent off of Girsu to prevent your opponent from possibly using it as Link Material themselves. And finally, 1 Gravity Controller.
Side Deck: 3 Nibiru, the Primal Being, 3 Thunder King, the Lightningstrike Kaiju, 1 Called By the Grave, 2 Lightning Storm, 3 Evenly Matched, and 3 Solemn Judgment.