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