This achievement is for taking Flash the Dog (The greatest gadget in the game, IMO) for a walk totaling 10km. Thankfully, this is a CUMULATIVE achievement and can be won over several games. You can check your progress by going into Stash, My Profile, Gadgets, Distance Run By Dog. Once that reaches 10,000m, the achievement should pop.
Flash himself is in the last tier of gadgets, so unlocking him will take quite a while and a LOT of coins, and he is worth 7000 coins. Good luck!