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