Here is the full list of all 51 Heliborne trophies - there are 43 bronze, 5 silver, 2 gold and 1 platinum.
Unlock all other trophies.
Research your first helicopter
Deploy all soldiers from Long Huey during a landing
Lose a night map battle
Have teammates destroy 50 targets with your mortars during single match
Earn awards: "Manpad hunter", "RPG hunter" and "Mortar hunter"
Earn "Mortar hunter" award
Earn "Manpad hunter" award
Earn "Air combat master 1st class" award
Earn "Sniper" award 50 times
Research all 1st and 2nd generation US helicopters
Fully research all variants of 1st and 2nd generation US helicopters
Research all 1st and 2nd generation Soviet helicopters
Completely research all USSR helicopters of all generations
Fully research all variants of USA helicopters
Completely research all Krokodil-A, Hv-24V, Hv-24P, Hv-24VM helicopters and their variants
Completely research all Adder helicopters and their variants
Fully research all 4th generation Russian helicopters and their variants
Deploy all troops from a Boxcar during a single sortie
Deploy all soldiers from PS-47 during one sortie
Deploy all troops from an Jolly Giant during a single sortie
Earn all game awards at least one time each
Have your White Eagle shot down while playing the Afghanistan, Khost province map
Get grounded having all 3 helicopters in your squadron under repair
Research all variants of the Swallowtail helicopter
Win a battle with a custom squadron consisting of only Zhukovsky and Dogfish
Win a battle with a custom squadron consisting of only Shortbow and Crossbow
Win a battle with a custom squadron consisting of only Chaos and Strife Night
Win a battle with a custom squadron consisting of only Crossbow and Absaroka Warrior
Win a battle with a custom squadron consisting of only Chaos, Hv-8MTV, Hv-8AMTSH variants
Win a battle with a three helicopter squadron customized from the Sg-60, Sg-6M, MC-500, Shortbow group.
Win a night map battle using custom squadron with only Zhukovsky
Win a battle with a custom squadron consisting only of three helicopters with coaxial rotors
Win a night map battle
Win a Co-Op battle
Win a solo Co-Op battle on Hard difficulty
Win a Co-Op battle on 4th generation map set to Very Hard difficulty
Shoot an enemy helicopter down using Hooligan
Shoot an enemy helicopter down using Sg-6M
Destroy 50 enemy vehicles during one battle
Shoot an Shortbow down using Phalanx
Win a battle using a custom squadron consisting of only recon helicopters
Shoot an enemy down using Coney
Shoot an enemy down using AM-21
Pick up at least one previously deployed trooper
Bring back and turn in for repairs helicopter with at least 3 destroyed modules
Earn a prototype helicopter
Shoot an enemy down using door gunners of the Chato
Deploy 8 MANPADs within 70 meter radius
During a single sortie, exhaust all ammunition of an attack helicopter
Avoid a MANPAD launch or an air-to-air missile