This is one way to go up Whale mountain. Probably the longest.
Follow the signs Pictograph Trail, and park at the Pictograph parking.
Start the hike along the Pictograph Trail, after about 0.7 mile turn left (North) into another canyon, follow the wash up.
After another mile turn right (North/East) into a small canyon with boulders.
There are some boulders in the wash, look before you hike, find a way around them.
Not too difficult but you need some experience scrambling up and down boulders.
You can follow this canyon all the way up (easier) or turn right out of the canyon, just before you hit the larger boulders.
This is a bit of a scramble, up the steeper canyon wall. Plenty of rocks, so take your time finding the right route.
A short climb up to the peak, the path is normally well marked with rock cairns.
In case you wondered, if you are in the right place, there is a new Whale Peak sign close actual to the peak.
The good part, stretches of the hike are on a fairly good hiking trail, especially on the return trip.
And it's a lot easier coming down on the boulders than going up.