This only seems to count when you start the climbing process. When there is someone sitting and waiting for you to accept the climbing it won't count for the achievement.
10 climbs isn't too bad and will come with regular gameplay. If you wan't it quick just go to every climbing spot that you see (the green marks on walls) and when someone accepts and has pulled you up just go back down, start another climbing process and hope that someone will join in again.
This achievement is cummulative over multiple matches and you can check your progress unter the challenges tab.
From the main menu select PROGRESS, RB to CHALLENGES, right column stripes, scroll down to A FRIEND IN NEED. It says x / 10.