You normally only hear "pull [something] off" or "pull off [something]". If I bowled three batsmen out in one innings (fat chance), I'd say that "I'd pulled off a hattrick".

"Pulling" is also used without the "off". Usually it's a "fast one", i.e. you have succeeded in beating someone at or to something, usually with an element of slyness. So, if I distract someone while I snaffle the last bagle, I'd say "I'd pulled a fast one over [someone]".

You don't usually hear any other usage. Leastways, not in the restricted circles I rotate in ...