You can earn Transmutation Crystals from the following activities:

Guaranteed drops:

Random Daily LFG
Undaunted Pledges
Trial Weekly Quests
Arena, Trial, and Battlegrounds Leaderboards
Alliance War Campaign End Rewards
Your first Rewards for the Worthy in a day
Maelstrom Arena (Veteran mode only)
Dragonstar Arena (Veteran mode only)
Chance to drop:

Dungeon Final Bosses
Rewards for the Worthy mails, after your first for the day
Random LFGs after your first
Note that while some activities are guaranteed to reward Transmutation Crystals, others only have a chance. For example, you will always receive Transmutation Crystals for completing your daily Undaunted Pledges, but you will only have a chance to receive them for defeating a dungeon's end boss.