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