Here is the full list of all 27 Azur Lane Crosswave trophies - there are 14 bronze, 4 silver, 8 gold and 1 platinum.
You've completed Azur Lane: Crosswave!
You've completed the Gallery Mode!
You've seen every character's Episodes!
You've repelled all rival fleets!
You've viewed all events that can occur in Story Mode!
You've completed the Final Chapter's report!!
You've made your first Pledge!
You've succeeded in Cognitive Awakening!
You've viewed the ending of Story Mode!
You've completed Chapter 6's report!
You purchased goods from Shiranui!
You've completed Chapter 5's report!
Strengthened a Skill!
You've acquired a very rare piece of equipment!
You've completed Chapter 4's report!
You've completed Chapter 3's report!
You've completed Chapter 2's report!
You've defeated countless enemies!
You've completed Chapter 1's report!
You achieved victory with an excellent rank!
You completed a rigging change!
You've added a new ally!
You responded to Akashi's request!
Brave new waters with your excellent Secretary Ship!
Report: Recording Initialized.
You achieved victory with the highest rank!
You've just begun the fun with your Secretary Ship.