This Seeking Tech guide will show you how to get the Cleared: Metal Slug 4 trophy from the PlayStation 4 version of Metal Slug Anthology.
This will unlock when you beat all six levels in Metal Slug 4.
Make sure you set the Continue setting to Free Play, which should grant you unlimited lives. You can also lower the difficulty if you want. There is no save option, so you need to beat the game in one go.
You can find the video playthrough, along with the time stamps, below:
0:28 Mission #1
5:12 Mission #2
13:19 Mission #3
17:46 Mission #4
25:22 Mission #5
33:27 Final Mission