Here is the full list of all 24 ALLTYNEX Second achievements.
1 credit cleared at Normal or higher difficulty with return shot mode on
1 credit cleared
Return Shot Mode unlocked
1 credit cleared with Type-B Craft
Score Over 10,000,000
Shoot down 10,000 enemies
Type-B Craft rolled out
Visitor Defeated
Mission accomplished
Encounter the Omega Javelin
Ophiuchus Husk Defeated
Alacran Defeated
Ajattara Defeated
Score Over 6,000,000
Adoni Defeated
Zoldyzant Defeated
Score Over 3,000,000
Shoot down 1,000 enemies
Aseliel Defeated
Slash an enemy with a 16x multiplier
Obtain 25,600 point combo bonuses 10 times in a row
Score Over 1,000,000
Shoot down 100 enemies
First campaign