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 made your first Pledge!
You've succeeded in Cognitive Awakening!
You've acquired a very rare piece of equipment!
You've viewed all events that can occur in Story Mode!
You've completed the Final Chapter's report!!
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've completed Chapter 3's report!
You've completed Chapter 2's report!
You've defeated countless enemies!
Strengthened a Skill!
You've completed Chapter 1's report!
You achieved victory with an excellent rank!
You've added a new ally!
You purchased goods from Shiranui!
You responded to Akashi's request!
You completed a rigging change!
Report: Recording Initialized.
You achieved victory with the highest rank!
Brave new waters with your excellent Secretary Ship!
You've just begun the fun with your Secretary Ship.