DRAGON QUEST XI S: Echoes of an Elusive Age - Definitive Edition

The description for this achievement is very misleading. What you actually need to do is ride on 6 DIFFERENT species of mounts. Variations of mounts do not count towards the achievement. You cannot keep mounting the same monster over and over again either.

This is likely because the original PS4 version trophy requires to ride every mount and at the time there were only 6 different species of mounts available. However, with the definitive edition, more mounts have been introduced so you are able to unlock the achievement much sooner.

Anyway, here is a list I have compiled in chronological order of appearance:

Mount Name - Location
Eggsoskeleton - Kingsbarrow

Skull Rider's Steed - Cryptic Crypt

Midnight Horknight - Laguna de Gondolia

Horknight's Hornet (Midnight Horknight Alternative Form) - Dundrasil Region

Metal Slime Knight
- The Champs Sauvage
- Insula Orientalis

Demon Rider (Skull Rider's Steed Alternative Form) - The Eerie Eyrie

Face Invader - Snaerfelt

Runny Eggsoskeleton (Eggsoskeleton Alternatve Form) - The Arborian Highlands

Iron Maiden - The Costa Valor (Act 2 Onwards)

Dragon Rider's Dragon - Mount Pang Lai: Base Cave (Act 2 Onwards)

Honeyhead Horknight (Midnight Horknight Alternative Form) - Mount Pang Lai: Slopes (Act 2 Onwards)

Vicious Horknight's Hornet (Midnight Horknight Alternative Form) - Dundrasil Region (Act 2 onwards)

Vicious Demonrider's Steed (Skull Rider's Steed Alternative Form)
- Dundrasil Region (Act 2 onwards)
- The Disciple's Trial: The Cruel Crypt (Act 3 Onwards)
- The Disciple's Trial: The Eerie Valley (Act 3 Onwards)

Gold Golem - The Gyldenhal (Act 2 Onwards)

Vicious Face Invader (Face Invader Alternative Form)
- The Snaerfelt (Act 2 Onwards)
- Drunstan's Labyrinth (Act 3 Onwards)
- Citadel of Spire (Act 3 Onwards)

Dragooner's Dragon (Dragon Rider's Dragon Alternative Form) - The Battleground (Act 2 Onwards)

Headless Horseman - Gallopolis Desert/Dundrasil Region (Act 2 onwards)
You might be able to get this after Honeyhead Horknight but cannot confirm.

Visor Kaiser (Face Invader Alternative Form)
- Mount Fuji
- Fortress of Fear (Act 2 onwards)

Golden Girl (Iron Maiden Alternative Form) - Fortress of Fear (Act 2 Onwards)

Hard-Boiled Eggsoskeleton (Eggsoskeleton Alternative Form) - Fortress of Fear (Act 2 Onwards)

Dread Dragoneer's Dragon (Dragon Rider's Dragon Alternative Form)
- Fortress of Fear (Act 2 Onwards)
- The Disciple's Trial: The Eerie Valley (Act 3 Onwards)

Hellrider's Steed (Skull Rider's Steed Alternative Form) - Fortress of Fear (Act 2 Onwards)

Horknight Watchmen's Hornet (Midnight Horknight Alternative Form)
- Hotto Steppe
- Dundrasil Region (Act 3 Onwards)

Malicious Skull Rider's Steed (Skull Rider's Steed Alternative Form) - Cryptic Crypt (Act 3 Onwards)

Malicious Dragoneer's Dragon (Dragon Rider's Dragon Alternative Form)
- The Battleground
- Insula Centralis (Act 3 Onwards)

Malicious Visor Kaiser (Face Invader Alternative Form) - Mount Fuji (Act 3 onwards)

Malicious Masqueraider (Face Invader Alternative Form) - The Snaerfelt (Act 3 onwards)

Glacial Golem (Gold Golem Alternative Form) - The Snaerfelt (Act 3 onwards)

Healdess Norseman (Healdess Horseman Alternative Form) - The Snaerfelt (Act 3 Onwards)

Malicious Slime Knight (Metal Slime Knight Alternative Form) - The Costa Valor (Act 3 Onwards)

Malicious Dragon Rider's Dragon (Dragon Rider's Dragon Alternative Form)
- Mount Pang Lai: Base Cave (Act 3 Onwards)
- Summit Tunnel (Act 3 Onwards)

Malicious Rotten Eggsoskeleton (Eggsoskeleton Alternative Form) - The Eerie Eyrie (Act 3 Onwards)

Malicious Honeyhead Horknight (Midnight Horknight Alternative Form) - Mount Pang Lai: Slopes (Act 3 Onwards)

Vicious Golden Girl (Golden Girl Alternative Form) - Citadel of Spite (Act 3 Onwards)

Vicious Hard-Boiled Eggsoskeleton (Eggsoskeleton Alternative Form) - Citadel of Spite (Act 3 Onwards)

Vicious Golden Girl (Golden Girl Alternative Form) - Citadel of Spite (Act 3 Onwards)

Vicious Hellrider's Steed (Skull Rider's Steed Alternative Form) - Citadel of Spite (Act 3 Onwards)

NOTE 1: I went off of memory for most of the list but will update it when I can. For the most part, you should get the achievement when you mount the Iron Maiden in The Costa Valor assuming you have mounted every single one up to that point.

NOTE 2: I'm not sure if the Vicious and Malicious variants actually count. When you kill them, the game doesn't describe them as Vicious or Malicious when showing that you can ride them in the text box. I will include them just in case.