Here is the full list of all 41 SMITE trophies - there are 19 bronze, 19 silver, 2 gold and 1 platinum.
Get 50 killing sprees in qualifying matches. (Versus or Ranked)
10 Gods Mastered.
Shut down 10 killing sprees in qualifying matches. (Versus or Ranked)
Get 10 double kills in qualifying matches. (Versus or Ranked)
Destroy a tower before 8 minutes in Conquest or Siege. (Versus or Ranked)
25 Joust 3v3 matches played. (Versus)
25 Arena matches played. (Versus)
Completed a match with a god from all Pantheons. (Versus or Ranked)
Kill an enemy god after they had already killed you. (Versus or Ranked)
Kill 100 gods in qualifying matches. (Versus or Ranked)
Get 100 assists in qualifying matches. (Versus or Ranked)
100 Minions killed. (Versus or Ranked)
Win an Arena match with more than 100 tickets remaining. (Versus)
You have acquired all Trophies! Congratulations!
5 Mastered Assassins.
5 Mastered Guardians.
5 Mastered Hunters.
5 Mastered Mages.
5 Mastered Warriors.
25 Assault matches played. (Versus)
25 Conquest matches played. (Versus)
Get 10 first blood accolades in qualifying matches. (Versus or Ranked)
Get 5 triple kills in qualifying matches. (Versus or Ranked)
Destroy 50 towers in qualifying matches. (Versus or Ranked)
Kill 3 enemy gods with a single ability. (Versus or Ranked)
Kill 5 enemy gods with a single ability. (Versus or Ranked)
Kill enemy gods more than 20 times in a single match, and only die once. (Versus or Ranked)
Deliver the killing blow on a map objective where enemies did more damage in a qualifying match. (Versus or Ranked)
Reach Level 30.
You have earned First Blood in any game mode before 0:00 on the in-game clock. (Versus or Ranked)
You killed more than 20 enemy gods in a single Conquest match. (Versus or Ranked)
Your team killed the Fire Giant in Conquest within 30 seconds of it spawning. (Versus or Ranked)
Your team killed the Gold Fury in Conquest within a minute and a half of it spawning. (Versus or Ranked)
1 god at Mastery 10.
1 League match played. (Ranked)
Get a quadra kill in a qualifying match. (Versus or Ranked)
Get a penta kill in a qualifying match. (Versus or Ranked)
Get 25 killing blows on map objectives in qualifying matches. (Versus or Ranked)
30 Gods Mastered.
50 Gods Mastered.
70 Gods Mastered.