Here is the full list of all 51 Call of Duty: Modern Warfare Remastered trophies - there are 34 bronze, 15 silver, 1 gold and 1 platinum.
Kill 2 enemies by blowing up a car in the single player campaign.
Complete 'All Ghillied Up' and 'One Shot, One Kill' on Veteran difficulty.
Carry Cpt. MacMillan to safety.
Kill at least 3 rappelling enemies in a single rope.
Kill Makarov and complete your mission
Complete 'All Ghillied Up' without alerting any enemies.
Complete 'Safehouse' on Veteran difficulty.
Find Al-Asad's safehouse.
Complete 'Shock and Awe' on Veteran difficulty.
Kill 4 enemies in a row with headshots in the single player campaign.
Kill 20 enemies with explosives in a single level.
Complete 'The Bog' and 'War Pig' on Veteran difficulty.
Operate an AC-130 gun ship.
Complete 'Hunted' and 'Death From Above' on Veteran difficulty.
Kill 5 enemies with one shot while in the AC-130 gunship.
Kill an enemy while blinded by a flashbang in the single player campaign.
Survive a dog attack.
Protect 'War Pig', the Abrams tank.
Save Pvt. Roycewicz on the stairs.
Complete 'Charlie Don't Surf' on Veteran difficulty.
Complete 'Blackout' on Veteran difficulty.
Kill the power.
Stab an injured crawling enemy.
Complete 'Crew Expendable' on Veteran difficulty.
Infiltrate a cargo ship.
Complete any level using only the knife to kill enemies.
Complete any level without reloading your weapon (excluding 'The Coup' and 'Aftermath').
Complete 'F.N.G.'.
Beat IW best time on the Ship Training course in 'F.N.G.' (15.1 sec).
Complete the cargo ship mockup in less than 19 seconds.
Earn all available trophies for Call of Duty®: Modern Warfare® Remastered.
Corner Zakhaev's Son.
Complete the game on any difficulty.
Find 15 enemy intel items.
Find 30 enemy intel items.
Destroy all the TVs showing Al-Asad's speech.
Save the farmer.
Sky dive to safety on Veteran difficulty.
Complete the game on Hardened or Veteran difficulty.
Complete 'Heat' and 'The Sins of the Father' on Veteran difficulty.
Complete 'Ultimatum', 'All In', and 'No Fighting in the War Room' on Veteran difficulty.
Complete 'Game Over' on Veteran difficulty.
Shoot down an enemy helicopter with an RPG in the single player campaign.
Kill 3 enemies in a row with your knife in the single player campaign.
Get a kill with each type of handheld gun, explosive and launcher in the single player campaign.
Destroy 8 enemy helicopters in 'Heat'.
Find the Desert Eagle in 'Crew Expendable' and kill 5 enemies with it.
Kill 20 attack dogs with a knife.
Find and use the hidden cache in 'Heat'.
Kill all 4 tanks on the overpass with the Javelin missile in 'The Bog'.
Alert the enemy helicopter in 'All Ghillied Up' and take it down.