How might I go about using parkour in pathfinder?

[MonkeySage]

My acrobatics is +15, my climb is +10, but my character is an elven monk with no climb speed. His movement speed is 45 ft.

[Gallowglass]

Take one of many ways to add a Divine Domain and add the Travel Domain. It has a special that lets you ignore difficult terrain x times a day. As Parkour is, basically, moving quickly and efficiently through difficult terrain, that gets the meat of it.

[Mehangel]

Use Spheres of Might, and take the Athletics sphere, focusing in the leap package w/ dips into the run and climb packages.

[Gallowglass]

...Find a GM who builds complex three dimensional battlemats with lots of terrain and obstacles and who responds to you saying "I'm going to run and jump toward that wall, plant my right foot and rebound up and to the left, then grab the rail and use my momentum to vault over it" with "Okay, roll two athletics check DC 18 and 24. If you succeed the second by more than 5 then you can catch the enemy up there flat footed." instead of "Uh, well, that is probably beyond your 30' movement. Just go up the stairs."

[Particle_Man]

Isn't there a feat that lets you get extra goodies from the Acrobatics skill (basically, do what unchained rogues get to do, but only with one skill)?

Also, how much of "parkour" for you is "jumping around" and how much is "get from A to B as quickly as possible"? Because other options include flight, burrow and teleportation.

The Fleet feat can be taken multiple times if you want to up your base speed. Other monk feats: Spider Step, Cloud Step, the various Dimensional X feats in Ultimate Combat (if that is part of your definition of parkour).

[Geddy2112]

If you can jump high or far enough, it is equal to flight. The high jump monk power will help a lot, as you can get +20 to acrobatics+monk level+ always count as running for a jump. Ninja has the high jumper power which halves the DC for high jumps.

A +20 to acrobatics is 5ft to your high jump distance. With the high jump power at level 4 and a +15 in acrobatics, you have a +39 modifier to your jump. Even if you rolled a 1 on the check, that is an 10 ft vertical jump. If you take 10, thats a 12 ft vertical leap, easily getting you on top of most buildings.

Having a source of cheeta's sprint (https://www.d20pfsrd.com/magic/all-spells/c/cheetah-s-sprint/) is effectively one turn flight to jump great distances. With a base speed of 30ft, it is effectively a +108 to acrobatics. That's 27 feet to your high jump, or 21.5ft to a long jump.

[MonkeySage]

By parkour I meant getting from point A to point B as quickly as possible. My character is a Zen Archer- he uses a bow instead of fists, so being able to move around efficiently and find a close but well guarded vantage point helps.