Press L2+R and then X.
When flying to the destination, jump right before landing so you can gain momentum and speed.
Wall Runner
Perform a wall run a set number of times.
Near a wall, press R2 to run up.
Skimmer
Swing near the ground a set number of times.
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Speed Freak
Swing with speed exceeding 20 meters a second for the set number of seconds.
Free Fall
Dive for a set number of meters.
When jumping down from a building, press the left analog stick to dive directly down.
Free Runner
Free run for the set amount of time.
On the ground, hold R2 to free run.
Whiplash
Wall run around corners of buildings.
Trebuchet
Running up a wall, launch yourself in the air a set number of times.
While running up a wall, press X right before the roof.
Finish Him
Perform a finisher a set number of times.
When the focus bar is full, press circle + triangle.
Untouchable
Perform a perfect dodge a set number of times.
First, you will need to buy the skill.
The perfect dodge can be performed right before the enemy attacks, when indicator is blue.
Hang Tight
Web a set number of enemies to walls.
Use gadgets and the web to do that.
Amazing
Defeat a set number of enemies without losing HP.

Brawler
Perform a combo of 15 strikes or more a set number of times.
Champion
Perform a combo of 30 strikes or more a set number of times.
Combowned
Perform a combo of 50 strikes or more a set number of times.
Home Run
Push a set number of enemies from buildings.
The Swing Kick skill is going to be particularly useful.
Pendulum
Perform a set number of Swing Kicks.
Zapped
Stun enemies with electricity.
Use the electric web.
Trapper
Stun or defeat a set number of enemies using Trip Mines.
Frequent Flyer
Fling a set number of enemies using the Web Throw.
Pull and throw the webbed or stunned enemy.
Thrown enemies stick to walls.
Hard Landing
Pull enemies from the air.
Launch enemies in the air and then pull them using square+cross.
Ascension
Pull enemies into the air.
Hold the triangle while in the air.
Judoka
Throw a set number of enemies with bare hands.
Press square and then hold the triangle.
Hit the enemy and toss them in any direction.
Demoted
Disarm the set number of enemies armed with guns or truncheons.
Once you unlock the ability to disarm enemies, hold the triangle to do that.
I’ll take that
Disarm the set number of enemies armed with rifles, rocket launchers or shields.
Duelist
Perform a set number of perfect strikes.
You must unlock the Perfect Hit skill.
Take Five
Constrain a set number of enemies with the web.
Only then the challenge may be completed.
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