Where to find the Fake Dragon Titan and how to beat it?

Pokémon Scarlet and Violet has three separate storylines. The Path of Legends Storyline takes you fighting Titan Pokémon that you can challenge in nearly any order, but there is one you cannot challenge first, not because of some story progression, but because of what you need to get there; the Fake Dragon Titan can be the very second Titan you can challenge, but taking the difficulty level into account, it should be the last one.

Where to find the Fake Dragon Titan?

The Fake Dragon Titan appears in Casseroya Lake, on the eastmost island. There will be several Tatsugiris doing nothing, but there will be one slightly larger than average at the south point of the island shouting "Taitaaan!"; interact with it, and the battle will start, but with a twist.

Battling the Fake Dragon Titan

Battle

Before you can battle the Titan Tatsugiri, it will be swallowed by a Dondozo (not a Titan), and you have to fight it twice, once by yourself and once with help from Arven.

Dondozo

Dondozo is level 56 with the Oblivious ability, which prevents it from being infatuated, falling for taunts, or being affected by Intimidate; being water-type, it is weak to Electric and Grass-type moves and resistant to Fire, Ice, Steel, and Water-type moves.

On the first fight, it will have the moves Aqua Tail, Body Slam, and Knock Off, and on the second fight, it will also use the move Order Up, which will give it an Attack Boost as Tatsugiri is a Curly one; and Body Slam may cause paralysis.

Tatsugiri

Unlike the other Titans, this time there are three battles, as you had yet to challenge the Titan, Tatsugiri; it is level 57 and is Dragon/Water-type, weak only to Dragon and Fairy-type moves, and resistant to Fire, Steel, and Water-type moves.

Tatsugiri will have the moves Muddy Water, Icy Wind, Dragon Pulse, and Taunt; Muddy Water may lower your accuracy, Icy Wind will reduce your Speed, and Taunt prevents you from using non-damaging moves.

After the Battle

After defeating the Fake Dragon Titan, your Koraidon/Miraidon will gain the Climbing ability, it will stick to almost any vertical surface, and Tatsugiri will appear again on the first island it appeared on for you to try and catch it; it will have the Titan Mark, which grants it the Former Titan title.