This one has a few prerequisites to even get access to the battle.
First, you have to max out Margaret's Social link.
Next, you have to defeat the optional bosses in all the dungeons up to Heaven (and this will have to be done by Feb. 5th at the latest).
Then you have to be on the path to the true ending, because you cannot fight her without opening that up.
To get the invitation to battle her you want to go through the events on 3/20 as normal for the true ending. So you go talk to Dojima and Nanako, but say you aren't done yet. Then head to Junes. Normally after the stuff in Junes and another chat with Dojima you'd talk to the gas station attendant to start off the true ending. Before doing this go into the Velvet Room and you should find Margaret alone. Then she'll challenge you to a duel.
From there progress as normal to the true ending and before going off to find Izanami head to the top floor of Heaven and battle Margaret. If you didn't get the Aqua Invitation before talking to the gas station attendant, you missed your chance for this battle and will have to reload a previous save.
Expect a very long and difficult battle. What difficulty you are on doesn't matter for the trophy, only what sort of a challenge you want. If you are doing it on anything but very easy, you'll want extremely high levels and the best personas possible to even stand a chance. Have plenty of healing items and make sure you have someone who is able to heal (preferably the whole party at once because Margaret uses a lot of full party damage skills).
Now one thing of note, some guides do say you have to have seen the true ending to get this, that is incorrect. I personally missed the true ending my first run and got this to happen on my second just fine. In fact I got this trophy before the one to defeat the true final boss.
Also, if you need help with maxing her S. Link, I found the FAQ section of this guide helpful:http://www.gamefaqs.com/vita/641695-persona-4-golden/faqs/64...