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 at least 3 rappelling enemies in a single rope.
Shoot down an enemy helicopter with an RPG in the single player campaign.
Find the Desert Eagle in 'Crew Expendable' and kill 5 enemies with it.
Complete any level using only the knife to kill enemies.
Complete any level without reloading your weapon (excluding 'The Coup' and 'Aftermath').
Complete 'All Ghillied Up' without alerting any enemies.
Kill 20 attack dogs with a knife.
Survive a dog attack.
Find Al-Asad's safehouse.
Kill 20 enemies with explosives in a single level.
Operate an AC-130 gun ship.
Kill 5 enemies with one shot while in the AC-130 gunship.
Protect 'War Pig', the Abrams tank.
Kill an enemy while blinded by a flashbang in the single player campaign.
Kill all 4 tanks on the overpass with the Javelin missile in 'The Bog'.
Kill 3 enemies in a row with your knife in the single player campaign.
Save Pvt. Roycewicz on the stairs.
Stab an injured crawling enemy.
Kill the power.
Infiltrate a cargo ship.
Complete 'F.N.G.'.
Earn all available trophies for Call of Duty®: Modern Warfare® Remastered.
Carry Cpt. MacMillan to safety.
Corner Zakhaev's Son.
Complete the game on any difficulty.
Find 15 enemy intel items.
Find 30 enemy intel items.
Complete the cargo ship mockup in less than 19 seconds.
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 'Crew Expendable' on Veteran difficulty.
Complete 'Blackout' on Veteran difficulty.
Complete 'Charlie Don't Surf' on Veteran difficulty.
Complete 'The Bog' and 'War Pig' on Veteran difficulty.
Complete 'Hunted' and 'Death From Above' on Veteran difficulty.
Complete 'Shock and Awe' on Veteran difficulty.
Complete 'Safehouse' on Veteran difficulty.
Complete 'All Ghillied Up' and 'One Shot, One Kill' on 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.
Kill 2 enemies by blowing up a car in the single player campaign.
Kill 4 enemies in a row with headshots in the single player campaign.
Kill Makarov and complete your mission
Get a kill with each type of handheld gun, explosive and launcher in the single player campaign.
Destroy 8 enemy helicopters in 'Heat'.
Find and use the hidden cache in 'Heat'.
Beat IW best time on the Ship Training course in 'F.N.G.' (15.1 sec).
Alert the enemy helicopter in 'All Ghillied Up' and take it down.