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