Here is the full list of all 39 Alchemic Jousts trophies - there are 27 bronze, 6 silver, 5 gold and 1 platinum.
Win 100 Duels.
Win 10 Duels.
Win a Combat Joust only hitting the enemy Tower with Giant Elementals.
Win a Combat Joust only hitting the enemy Tower with Sand Elementals.
Win a Duel.
Hit the enemy Tower with a confused enemy Elemental.
Discover 50 Skills.
Get all the Trophies!
Finish the Campaign.
Discover 100 Skills.
Discover all the Skills.
Gain all Easy Stars.
Gain all Normal Stars.
Gain all Hard Stars.
Reach Level 10.
Reach Level 20.
Reach Level 30.
Generate 85 or more per second of a single resource during a Joust.
Cause a Slapocalypse!
Kill 15 Elementals with a single Meteorite.
Kill 6 Elementals with a single Electric Storm.
Hit the enemy Tower ground level with a flying Elemental.
Create 100 Elementals during a single Joust.
Create 500 Elementals during your playtime.
Create 1500 Elementals during your playtime.
Create 5000 Elementals during your playtime.
Kill 500 enemy Elementals during your playtime.
Kill 1500 enemy Elementals during your playtime.
Kill 5000 enemy Elementals during your playtime.
Obtain 15 Hard victories playing Combat Elite Jousts.
Obtain 15 Hard victories playing Capture Elite Jousts.
Obtain 15 Hard victories playing KotH Elite Jousts.
Obtain 10 Hard victories playing Attack Elite Jousts.
Obtain 5 Hard victories playing Endless Elite Jousts.
Win a Hard Combat Elite Joust without losing any Health on your Tower.
Win a Hard Capture Elite Joust without losing any Health on your Tower.
Win a Hard KotH Elite Joust without losing any Health on your Tower.
Hit 25 times or more on an Attack Elite Joust.
Survive 20 minutes or more on an Endless Elite Joust.