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