Here is the full list of all 50 LOST SPHEAR trophies - there are 39 bronze, 8 silver, 2 gold and 1 platinum.
Night and day restored.
Collected from Glow Spots 100 times.
Vulcosuit acquired.
In-battle move distance reached 1000D.
Made 15 weak-spot attacks.
Made 10 evasions.
Ship acquired.
Activated Momentum Mode 10 times.
Activated Momentum Mode 4 times in 1 battle.
Damaged 3 or more monsters with 1 attack.
All trophies earned.
Winger acquired.
Sea restored.
Royal Capital Marche restored.
Returned from the Fade Realm.
Landed on the moon.
Unlocked all spritnite columns.
Defeated Krom.
Defeated Eclipse.
Defeated Dark Ruin.
Obtained Moon's Soul.
Obtained Rainbow Spritnite.
Obtained Sunlight Spritnite.
Obtained Chrono Spritnite.
Obtained War Maiden Spritnite.
Obtained Tyranny Spritnite.
Obtained Raggys' Spritnite.
Obtained Isolation Spritnite.
Ate Clam Soup.
Ate Moon Tripe.
Ate Fruit Jelly.
Used Last Elixir.
Turned into rooster.
Money acquired reached 1,000,000G.
Made 10 Machine Kills.
Made 10 Momentum Kills.
Made 30 consecutive hits.
Caused 500 or more damage with 1 attack.
Caused 1,000 or more damage with 1 attack.
Made 100 critical hits.
Caused 10 sublimations.
Sublimated spritnite to max level.
Used all paradigm drives.
Defeated 300 monsters with Scan.
Went fishing 30 times.
Created spritnite 50 times.
Created 10 artifacts.
Ate 100 different foods.
Money spent reached 500,000G.
Total shop sales reached 100,000G.