Here is the full list of all 30 Hangeki achievements.
Beat a stage without dying
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 10 different weapons
Use 20 different weapons
Use 35 different weapons
Unlock and use 50 weapons
Beat stage 2
Beat stage 3
Beat stage 4
Beat stage 5
Beat stage 6
Beat stage 7
Beat stage 8
Beat stage 9
Beat stage 10
Beat all 16 challenges