This Seeking Tech guide will show you how to get the Cleared: Metal Slug 6 trophy from the PlayStation 4 version of Metal Slug Anthology.
You can unlock this by beating the game. To make things easier for yourself, you should set the Continues settings to Free Play, which should give you unlimited lives.
You can find a video playthrough, along with the time stamps, below:
0:16 Mission #1
5:54 Mission #2
13:42 Mission #3
24:30 Mission #4
32:06 Final Mission