When I played the game, I had couldn't do what many other threads suggested, so here is an alternative way: After opening the gate, hold Z-target towards far wall and take out your hook shot. Center the red dot under the target. Press the down arrow to raise the red dot above the target. When you let go of the Down key, the dot will slowly drift down, passing directly over the target.

moosic1323 : Hey, i just randomly clicked on this game for the first time in like a year, so I don't know if this is still an issue for you or not, but I'll give you my advice. I personally was stuck on that particular spot until someone made a thread (we're talking months later, lol). I believe it mentioned that there is now (or was, I haven't checked for a while) an option to take of snap or something like that when you double click the menu on the emulator. Turn off/on whatever grid/snap the game is using. This will allow you to freely move the cursor, but it should now be moving incredibly slowly. Use this for whenever a shot requires precision like this, but I think this was the only time. 

More convenient, yet more expensive solution: Get a controller. lol I ended up getting one for Sonic Generations but as far as this game goes I wish I cracked sooner. Anyways, hope this was of some help if you still needed it. If I can find the post I mentioned I'll edit this and add the link. But these are the ONLY 2 options that I know of to hit that target. 

And out of curiosity, does the menu take forever to pop up for you?

EDIT:
https://www.vizzed.com/boards/thread.php?id=12969&ppp=20&page=0#288000
Here's the link to the thread. Look at the second to last reply. Want you want to do has to do with "smooth x and y." That will turn off the snap function for the keyboard.

moosic1323 : Dude you're brilliant that Z targeting trick worked like a charm.

You are a genius! I've been stuck on this part for 5 months! THANK YOU!

Thank you moosic1323! I thought of giving up after trying and trying and then I searched Google for an answer and this came up.