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 Chapter 4's report!
You've completed Chapter 3's report!
You achieved victory with an excellent rank!
You've defeated countless enemies!
You purchased goods from Shiranui!
You've completed Chapter 2's report!
Brave new waters with your excellent Secretary Ship!
Strengthened a Skill!
You've just begun the fun with your Secretary Ship.
You've completed Chapter 1's report!
You responded to Akashi's request!
You've added a new ally!
Report: Recording Initialized.
You completed a rigging change!
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 Cognitive Awakening!
You've viewed the ending of Story Mode!
You've acquired a very rare piece of equipment!
You've completed the Final Chapter's report!!
You've completed Chapter 6's report!
You've completed Chapter 5's report!