Here is the full list of all 30 Hangeki achievements.
Beat stage 8
Beat stage 7
Use 10 different weapons
Beat stage 6
Beat stage 5
Beat stage 4
Beat stage 3
Beat a stage without dying
Beat stage 2
Beat stage 1
Beat all ten missions and save the galaxy
Reach wave 100 in endless mode
Beat a stage using Pulsar weapons
Beat a stage using Randivar weaponry
Beat a stage using Infernix brand firepower
Beat any stage using Crystalix branded weapons
Beat a stage using weapons supplied by The Pentaverat
Beat a stage using Hangeki Initiative weaponry
Effectively use the Thunder Edge in live combat
Beat the par time on all ten stages
Beat all ten stages with a second player
Beat Boss Rush All
Good luck beating everything
Descend into the Crypt
Use 20 different weapons
Use 35 different weapons
Unlock and use 50 weapons
Beat stage 9
Beat stage 10
Beat all 16 challenges