First you have to let them do whatever it is they do at their end to test your connection and confirm that, yes, it is dropping out, and yes, the speed is much lower than it should be. So you've established that you're not making shit up for no reason.
Then they try to fix it by changing some settings. I have no idea what they do at this stage, but it obviously isn't going to work when the problem is physical damage to the cable. You cannot get them to skip this stage, and it's going to cause you problems later, but you just have to deal with that then.
The next step is to pass you on to the next level of support, where they do some magic to confirm that there's physical damage to the line. Immediately they try to pass it off to Telstra. If they do this, you'll wait a week for Telstra to do anything, and TPG won't take any further acxtion until they hear back from Telstra. It should go without saying that you do not want this to happen.
If you argue enough you can convince them to send one of their own techs over to check the junction box and the cable from it to the flat. This tech will not have been told anything and will insist on checking the connection inside the flat to confirm that, yes, there is still a problem. They will then use their own modem to connect, to make sure that it's not your modem causing the problem (even though they already confirmed line damage).
Eventually they'll go outside and react with appropriate horror to the goddamn mess that is the building's junction box and the incredibly shoddy job someone did of connecting each flat to it. They'll do another test at the box and confirm that the connection there is fine, and finally conclude what you knew all along.
So they fix the cable and your internet's not dropping out any more. But it's still not working properly. The speed's fine, the connection stays up, but there's a weird delay before it starts loading anything. You can watch videos on YouTube, but you have to wait ten seconds or so before each video starts. You can't do anything about this now because TPG went ahead and contacted Telstra and are waiting to hear back.
Eventually Telstra contacts TPG and tells them there's no problem with the phone line. TPG will then contact you and ask you if you have a spare modem you can try. Of course you don't. They'll then offer to mail you one, for which you will pay postage, and will then have to return at your own expense. You don't want that, so you refuse and as a compromise they agree to continue monitoring your connection and call you back in a day or two to see if there are any more problems.
Finally, you get that last call, and you explain to them about the weird loading delays. Now, remember those settings they changed way back at the start? They'll quickly realise that those need to be changed back to what they were before, and once they do that your connection will magically work normally again.