Recommended Level: 50+
Likely to be your last stop on the Path of Legends, The Search for the False Dragon Titan requires a great deal of travel through Paldea. The average level of your team members also needs to be quite high to survive the Pokémon 'guarding' the Titan, so don't expect to tackle this one until you have a lot of other challenges under your belt.
The Search for the False Dragon Titan takes place at Casseroya Lake, located north of West Province (Area Two) and West Province (Area Three) and west of Glaseado Mountain. Though there is plenty of land to navigate in this area, you'll need to be able to swim to reach the Titan. This requires that you, at minimum, complete The Search for the Open Sky Titan.
Once you've ready to go, hop into Casseroya Lake on its east side, coming up from West Province (Area Two). Swim your way out to the nearest two islands to the northwest, which is further away than that suggestion sounds. On the smaller island you'll find an oversized Tatsugiri that won't attack. Speak to it and your foe, a massive Dondozo, will leap out of the water.
Dondozo, the False Dragon Titan
Despite its size the Dondozo Titan is not that difficult. It ccan hit relatively hard with Body Slam and Water Pulse, potentially confusing your Pokémon, but the Titan takes a great deal of damage to Grass- and Electric-type moves. You've probably been using one of those two types to ward off the Pokémon in the lake, so use it again here for a quick win.
Once you've depleted the Titan's health it will flee. Hop back in the water and surf west, to the larger, central island. There are shallows on the north side where you'll again find the Dondozo. Arven will join you for round two of the battle, and he'll bring along a Greedent that can use Take Down. The two of you should make short work of the Dondozo, even if it is stronger.
Alas, this is not the end of the battle...
Tatsugiri, the False Dragon Titan
The Tatsugiri was the real Titan? Or were they both...? Well, whatever. The Tatsugiri can use Dragon Pulse, which hits very hard, and Taunt, forcing your Pokémon to use only attack moves. It can also use Muddy Water to hit both your Pokémon and Greedent, though it's an inaccurate move. Putting in another Dragon-type to fight is feasible, though if it's not faster than the Tatsugiri it will probably get knocked out. A better bet is to use either a Fairy-type, which will be immune to the Tatsugiri, or a Steel-type, which will shrug off the Tatsugiri's moves. Fairy-, Ice-, and Dragon-type moves will bring the Titan down.
Defeating the two Titans will earn Arven the Spicy Herba Mystica, and you'll earn a Titan's Badge. Give it a sandwich and your Pokémon mount will now be able to climb up vertical surfaces, which will make a thorough exploration of Paldea much easier.