Here is the full list of all 10 Climber: Sky is the Limit achievements worth 1,000 gamerscore.
Summit Tutorial Mountain
Summit Manaslu
Summit Cho Oyu
Summit Gasherbrum
Summit Mount Everest
Summit K2
Summit Cho Oyu with no additional oxygen
Summit Gashemburg with no additional oxygen
Summit Mount Everest with no additional oxygen
Summit K2 with no additional oxygen