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