This is a walkthrough of the Trophy Hunter (Aspect of Hircine) quest.  NPC responses are paraphrased while PC options are kept the same (or very close) to the actual in game option.

To start the quest the player needs to have access to the Lore Master.  (TJH quest).

This walkthrough assumes that the player already knows (or during the quest figures out) how to ride large chain beasts. 

(The collector will give a hint on this if the PC asks about how to transport them.)

It also assumes the player already completed the Aspect of Mephala. This makes one of the activities less of a pain.

Besides making cool collectables, a statue enables you to walk around with a chain beast in your pocket. Safe ride whenever you need.

The Collector wants beasts of different races.

Besides the spiders (which occur in many tramps and possibly in the wild) the sample images (oldrim/LE page) hint at another location where you might find a mimic.

Note that all mimic are of the same race (Chain Crab). so the collector will not accept two of those, even if they different materials or mimicking a different item.

Chain fish are pretty rare and too small to ride (but too big to put in your pocket) so would be a pain to transport.

As noted there is that big mine near Whiterun also one of the other quests leads to encounters with another big chain beast.

There is also a secret option.