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