Here is the full list of all 17 Mobile Suit Gundam Battle Operation 2 trophies - there are 13 bronze and 4 silver.
Defeat a rival.
Sortie into battle 10 times.
Rank up to Rating D.
Rank up to Rating D+.
Rank up to Rating C-.
Rank up to Rating C.
Rank up to Rating C+.
Rank up to Rating B-.
Rank up to Rating B.
Rank up to Rating B+.
Acquire 10 MS.
Get promoted to Lance Corporal.
Get promoted to Corporal.
Get promoted to Sergeant.
Get promoted to Master Sergeant.
Complete "Exploring the base camp" training
Get promoted to Private First Class.