Here is the full list of all 45 F1 2013 achievements worth 1,000 gamerscore. It takes around 30-35 hours to unlock all of the achievements on Xbox 360.
You have set clean laps at Brands Hatch and Jerez in Time Trial with the Ferrari 312 T2.
You have completed 25 races online.
You have won the Constructors' Championship in Co-op.
You have won the Drivers' Championship in Co-op.
You elected to end R&D on the current seasons car in Career.
You have completed a Career race without colliding with another car or object.
You have completed 10 races using only the cockpit camera.
You have won an online race with a car from the Classic 80's at Jerez.
You have completed your first 100% race in Career or Grand Prix.
You won a race with all driver assists disabled.
You have completed three races in Split Screen.
You qualified last, but finished first in Career.
You moved to another team mid-season in Career.
You have won the Drivers' Championship in Career on any difficulty.
You have won the Constructors' Championship in Career.
You set the fastest lap time in every session of a long race weekend in Career.
You have taken pole position in Career.
You have performed a Mid-Session Save.
You have set a clean lap time for all circuits in Time Trial.
You have achieved gold in the Time Attack Classic 80's challenge.
You have earned a gold medal in all of the Time Attack scenarios.
You have posted a time in all of the Time Attack scenarios.
You have earned a gold medal in all scenarios in Scenario Mode.
You have set clean lap times at 5 different circuits in Time Trial.
You earned a medal in each scenario of Final Year in Scenario Mode.
You earned a medal in each scenario of Drivers' Championship in Scenario Mode.
You earned a medal in each scenario of Team Mate Challenge in Scenario Mode.
You earned a medal in each scenario of Rookie Driver in Scenario Mode.
You have earned a medal in Scenario Mode.
You stayed with the same team through the whole season in Season Challenge.
You returned to your starting team in Season Challenge.
You have won the Drivers' Championship in Season Challenge on hard difficulty.
You have won the Drivers' Championship in Season Challenge.
You have taken pole position in One-Shot Qualifying.
You raced for five different teams in Season Challenge in a single season.
You have beaten four rivals in one season in Season Challenge.
You passed all of your objectives over a race weekend in Season Challenge.
You finished a race in the top three in Career or Season Challenge.
You have beaten your first rival in Season Challenge.
You have set a valid lap time in One-Shot Qualifying.
You have earned a gold medal in each Young Driver Test.
You have successfully completed all of the Young Driver Tests.
You have completed all Day 1 tests in the Young Drivers Test.
You have earned a gold medal in a Young Driver Test.
Complete 50 online races.