Whenever you climb a wall as Wolf Link you see a small animation of grabbing the ledge and climbing up. In a few places this animation is skippable saving a bit of time.
A nearby wall will interfer with the animation due to clipping and cancel it.
*Note: For now some pictures are taken in TPSD and therefore look a bit different - the quick climbs still work the same in TPHD.
While collecting the tears for Eldin Vessel, approach the ledge hugging the wall and climb up angled slighty left.
During MDH right after burning the first web as wolf climb up the first ledge normally. Then go right and climb up roughly around the middle of the last stone brick on the right side.
Just before your first meeting with Skull kid, climb the ledge right in the corner angled slightly to the left.
Right before getting to the Boss Key using Early Boss Key, climb up right where the spinner track meets the solid ground angled to the right.
NOTE: Sometimes you can clip out of bounds while using this Quick climb causing you to void out.
While climbing Snowpeak Mountain there are two possible Quick Climbs in quick succession.
For the first one climb the ledge walking right into the corner betweeen mountain and wall.
For the second one just climb up using the right corner.