Felspider
Source: Pet Battle. It's just like a regular spider, but fel. Beast type. Easiest way I found to obtain the felspider. Go to the Pits of Despair, west of Illidari Perch.
Felspider is a wild battle pet from the Legion expansion, found in Azsuna on the island of Faronaar near the Pits of Despair, west of Illidari Perch.
Guide awaiting review
Travel to Azsuna
Head to Azsuna and make your way to Illidari Perch. From there, follow the road up and over the NPCs — you will appear to be riding along the overhang of a cave as you head toward the west side of the island.
Climb the Hill
Begin your ascent at 35.13, 41.47 in Azsuna, which is the easiest point to start climbing the hill toward the spider spawn area.
Find Felspiders on the Hill
A few Felspiders spawn on top of the hill at 24.3, 46.8 in Azsuna, roughly under the 'F' in 'Faronaar' on your map. Avoid the east side of the island, as Felspiders rarely spawn there and some that do are inaccessible under trees.
Alternatively, Use the Green Portal
From the Pits of Despair, take the green portal at 26.7, 41.4 to reach the Soulrender area. Walk through the building to the opposite side, stand at the ledge, and jump down to the rocky area below where many tameable Felspiders roam — use a glider for the long fall. Hunters with the Eagle Ally can fly directly to the Faronaar Eagle and walk down to this area.
Tips
The Felspider battle pet respawn timer exceeds 15 minutes, so expect downtime between spawns when hunting for a blue quality pet.