Here is the full list of all 24 ALLTYNEX Second achievements.
Aseliel Defeated
Shoot down 100 enemies
First campaign
Slash an enemy with a 16x multiplier
Obtain 25,600 point combo bonuses 10 times in a row
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 1,000 enemies
Shoot down 10,000 enemies
Zoldyzant Defeated
Adoni Defeated
Ajattara Defeated
Alacran Defeated
Ophiuchus Husk Defeated
Visitor Defeated
Score Over 1,000,000
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