Here is the full list of all 20 THEXDER NEO trophies - there are 19 bronze and 1 silver.
Destroyed all enemies in Level 10.
Completed Level 10 on Easy Mode.
Destroyed all enemies in Level 9.
Destroyed all enemies in Level 8.
Destroyed all enemies in Level 6.
Destroyed all enemies in Level 5.
Destroyed all enemies in Level 4.
Destroyed all enemies in Level 3.
Destroyed all enemies in Level 2.
Completed a level without using shields.
Destroyed all enemies in Level 1.
Played THEXDER NEO and entered Nedium.
Invited someone.
Completed Level 10 on Normal Mode.
Completed Level 50 on Normal Mode.
Completed Level 100 on Normal Mode.
Uncovered all secret enemies.
Won first place in Online Play.
Destroyed all enemies in Level 7.
Completed playthrough (16 levels) of Classic Version.