Speak to the Minstreling Wanderer, in The Crystarium (7.6, 12.5). Shadow Gwiber is unlocked from a rare drop item, the Shadow Gwiber Trumpet, which has a chance to drop from the new Extreme Trial, The Minstrel's Balad: Hades's Elegy. That alone puts it out of reach for most players. Acquiring it will take top-tier gear, skill, some friends, and a good amount of luck. Throw together a dragon, a freaking dinosaur, and just the right amount of edge, and you've got this awesome mount. You'll need to achieve the second-highest reputation rank for it to become available. It takes a total of 18 Fae Fancies to purchase the Portly Porxie mount from the Pixie Vendor, located in Il Mheg (12.4, 32.9). Doing quests for them allows you to earn their new currency, Fae Fancies. After that, you can start doing quests for them. You'll need to complete this quest in order to unlock reputation with the Pixie Beast Tribe. Completing the quest called " The Wheel Turns." Afterward, you can speak with the Pink Pixie in the Crystarium (13.2, 15.3) and pick up the quest called " Manic Pixie Dream Realm." You'll first need to beat Titania in the Main Scenario Quests. In order to purchase the Portly Porxie, you'll have to start the new Pixie Beast Tribe Quests. Unfortunately, it will definitely take some time to unlock. Here's a mount that players have been clamoring over, and with good reason. Use them to buy the Forgiven Reticence Horn, which is then consumed to unlock the mount for your character. Once you have all 3,200 Nuts, you'll need to exchange them with a Nut Vendor, either of these will work: Previous Hunts and Elite Marks from prior expansions will not award you with any Sack of Nuts, so stick to hunting in Norvrandt. To start with, you'll need to earn 3,200 Sack of Nuts, a currency which is earned by participating in The Hunt for the Nutsy Clan and by killing Elite Marks in the Shadowbringers Expansion. Of the bunch, this mount is one of the more straightforward to get, but try not to laugh.
Gulg, although this version seems a bit tamer. This is more or less the winged, Lion-esque Sin Eater from the game's opening cutscene. However, if you're here for the Morbol mount featured on one of FFXIV's developer streams, that has not yet been released, so you won't find it here. Most of the new mounts listed below are unlocked through different means - some are easier than others.