Here is my way of catching them, and work every time, no running necessary.
- Tarantula have a 3 seconds hostile aggro time.
- When your close to one, dont move, wait about 3 second, and pull your net.
- The tarantula will raise his legs in an attacking position, again, wait 3 seconds , and legs go down
- You can now move toward it. Again you get less than 3 seconds, idealy move toward it for 2 seconds. Dont run, and dont try to move to fast too ( if your not too sure, you can hold A to keep your net in catching position, no effect on how the the tarantula aggro you )
- It will raise its legs again, repeat same pattern until your close enough to catch it.
Been doing that all night, sure might require some practice at first, but its very easy
Also been testing that, if you want to summon tarantula, no need to chop everything on island. Just make sure island got insects, take all the flowers ( no need to shovel ), all the fruits from tree, destroy all rocks, and your good to go.