Here is the full list of all 45 F1 2013 achievements. It takes around 30-35 hours to unlock all of the achievements on Windows.
Win the Constructors' Championship in Co-op.
Win an Online Race with any car from the Classic 80's at Jerez.
Win the Constructors' Championship in Career.
Win the Drivers' Championship in Career on any difficulty.
Earn a medal in each scenario of Final Year in Scenario Mode.
Complete 3 races in Split Screen.
Complete a Career race without colliding with another car or object.
Earn a medal in each scenario of Drivers' Championship in Scenario Mode.
Achieve gold in the Time Attack Classic 80's challenge.
Complete 10 races using only the cockpit camera.
Win a race with all driver assists disabled.
Earn a gold medal in each Young Driver Test.
Stay with the same team through the whole season in Season Challenge.
In Career, qualify last, but finish first.
Return to your starting team in Season Challenge.
Earn a medal in each scenario of Team Mate Challenge in Scenario Mode.
Set a clean lap time for all circuits in Time Trial.
Earn a medal in each scenario of Rookie Driver in Scenario Mode.
Race for five different teams in Season Challenge in a single season.
Beat four rivals in one season in Season Challenge.
Win the Drivers' Championship in Season Challenge.
Set the fastest lap time in every session of a long race weekend in Career.
Beat your first rival in Season Challenge.
Post a time in all of the Time Attack scenarios.
Set a clean lap at Brands Hatch and Jerez in Time Trial with the Ferrari 312 T2.
Successfully complete all of the Young Driver Tests.
Complete all Day 1 tests in the Young Drivers Test.
Set clean lap times at 5 different circuits in Time Trial.
Finish a race in the top three in Career or Season Challenge.
Take pole position in Career.
Perform a Mid-Session Save.
Pass all of your objectives over a race weekend in Season Challenge.
Take pole position in One-Shot Qualifying.
Set a valid lap time in One-Shot Qualifying.
Earn a medal in Scenario Mode.
Earn a gold medal in any of the Young Driver Tests.
Complete a 100% race in Career or Grand Prix.
Win the Drivers' Championship in Season Challenge on hard difficulty.
End R&D early on the current seasons car in Career.
Move to another team mid-season in Career.
Earn a gold medal in all of the Time Attack scenarios.
Earn a gold medal in every scenario in Scenario Mode.
Win the Drivers' Championship in Co-op.
Complete 25 online races.
Complete 50 online races.