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