Here is the full list of all 27 Azur Lane Crosswave achievements.
You've viewed all events that can occur in Story Mode!
You've completed the Final Chapter's report!!
You've succeeded in Cognition Awakening!
Strengthened a Skill!
You've viewed the ending of Story Mode!
You've completed Chapter 6's report!
You've completed Chapter 5's report!
You've completed Chapter 4's report!
You achieved victory with an excellent rank!
You purchased goods from Shiranui!
You've defeated countless enemies!
You've just started the fun days with your Secretary Ship.
Brave new waters with your excellent Secretary Ship!
You've completed Chapter 3's report!
You responded to Akashi's request!
You've completed Chapter 2's report!
You've completed Chapter 1's report!
You completed a rigging change!
You've added a new ally!
Report: Recording Initialized.
You achieved victory with the highest rank!
You've completed Azur Lane: Crosswave!
You've made your first Pledge!
You've seen every character's Episodes!
You've repelled all rival fleets!
You've completed the Gallery Mode!
You've acquired a very rare piece of equipment!