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