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Like most COD games trophies take a few minutes to pop

You should play through the campaign on recruit it’s short and the trophies won’t look legit otherwise as combat hardened will pop after you finish any mission but combat recruit and any other mission completion trophies won’t.

Combat Hardened: Load Final Countdown Mission on lowest difficulty when you finish you will unlock The Final Countdown, and Combat Hardened trophies.

Mind Trip and The Red Door: Load break on through and do what Adler says after the first scenario the trophy pops, keep playing until the red door is in the centre of the ruins then take the right path at the split and keep running until you are forced to open it.

Jack of all trades: Get one more kill with AR
Old faithful: Get one more kill with AR

Other challenge trophies you need to do your self but they are all easy.
Scorched earth
Scorched earth II
Patriot arrow
Firing range
Everyonnnnnee
Explosive finish

If you didn’t do the side missions or need the alternate ending trophy just use mission select and they pop on mission completion.