Here is the full list of all 45 STAR WARS: Battlefront Classic Collection achievements.
Reach legendary Marksman status
Reach legendary Frenzy status
Reach legendary Gunslinger status
Reach elite Marksman status
Reach legendary Regulator status
Reach legendary Technician status
Reach legendary War Hero status
Reach elite Gunslinger status
Reach elite Technician status
Reach elite Regulator status
Reach elite Frenzy status
Reach legendary Guardian status
Reach veteran Technician status
Reach legendary Demolition status
Reach General Rank
Reach elite Demolition status
Reach legendary Endurance status
Reach veteran Demolition status
Earn your first Demolition medal
Reach elite War Hero status
Complete the Battlefront II Campaign
Reach elite Guardian status
Reach elite Endurance status
Reach Captain Rank
Reach veteran Frenzy status
Reach veteran Gunslinger status
Reach veteran Regulator status
Reach veteran Marksman status
Reach veteran War Hero status
Reach Sergeant Rank
Earn your first Gunslinger medal
Reach veteran Guardian status
Reach veteran Endurance status
Earn your first Frenzy medal
Earn your first Marksman medal
Earn your first Regulator medal
Earn your first Endurance Medal
Earn your first War Hero Medal
Earn your first Technician medal
Earn your first Guardian Medal
Complete the Galactic Civil War Campaign in Battlefront
Take down an AT-AT with tow cables in Battlefront
Complete the Clone Wars Campaign in Battlefront
Defeat a Jedi hero by knocking them off the map in Battlefront
Complete all other achievements