Alrighty, according to the Preliminary Patch Notes there are 13 new minions, 7 mounts and one barding. Time to figure out how to get them. Some locations are known or fairly easy to guess, others are speculation. I am guessing 2 of the new minions will come from the new dungeons.
MINIONS
Wind-Up Gnath - Reward from Vath Beasrtment Quests at Reputation lvl 4
Wind-Up Vath - Reward from Vath Beastment Quests at Reputation lvl 7
Wind-Up Garuda - Crafted (WVR) - Blood Pepper, Chimerical Felt, Crawler Silk, Garuda's Feather, Wind Shard x99
Wind-Up Titan - Crafted (WVR) - Blood Pepper, Chimerical Felt, Crawler Silk, Titan's Heart, Earth Shard x99
Wind-Up Leviathan - Crafted (WVR) - Blood Pepper, Chimerical Felt, Crawler Silk, Leviathan's Barb, Water Shard x99
Wind-Up Nero Tol Scaeva - bought from the Gold Saucer for 30,000 MGP
Faustlet - Drops from Alexander: Midas 8 (Savage) - one item rolled on by party
Calco - Dungeon Drop - Antitower
Brena - Dungeon Drop - Antitower
Morpho - Dungeon Drop - Lost City of Amdapoor (Hard)
Poro Roggo - Quest Reward - MSQ "The Word of the Mother"
Spoony Bard - Bonus item with Heavensward Sountrack
Fenrir Pup - Randomly drops to inventory at end of a Feast PvP match.
MOUNTS
Kongamato Whistle - Reward from Vath Beastment Quests at Reputation lvl 7
Zu Horn - Bought from Bertana in Idyllshire (Wonderous Sundries I) costs 1 'Iron Voyage Spoil'
White Lanner Whistle - Small chance to drop from chest in Bismark (Extreme)
Rose Lanner Whistle - Small chance to drop from chest in Ravana (Extreme)
Round Lanner Whistle- Small chance to drop from chest in Thordan (Extreme)
Warring Lanner - Small chance to drop from chest in Containment Bay S1T7(Extreme)
Gloria Ignition Key - Achievement Reward - 200 wins in The Feast
Patch 3.25 Bennu - Cash Shop item (available March 30th)
Patch 3.25 White Fat Chocobo ?? - Reward from JP 7/11 Promotion - possibly coming to NA/EU somehow.
BARDING
Set of Sephirotic Barding - Crafted (LTW) - Sephirot Sap, Dinosaur Leather x4, Star Sapphire, Star Ruby x2, Earth Cluster x2, Wind Cluster x2
Patch 3.20 Egg Hunter Barding - Quest reward for 2016 Hatching Tide seasonal event
Patch 3.25 Race Barding - Achievement Reward (Ride to the Challenge I - Complete the first 15 Chocobo Challenge races.)