It requires TT, and I suggest filling your inventory full of items villagers are not interested in to prevent being pinged for other reasons. If she does ping you to move, and then changes her mind of staying, don't panic. Just turn off your game, and start up again for a new chance to convince her.
She could be flagged as semi-permanent villager by the game in your town, just like Tom in my town who refused to move out for approx. 4 months. The simplest thing you could do is just totally ignore her; do not fulfill her requests and don't talk to her at all.
Another way is Time Traveling, but there might be a chance your other villagers moved out instead of Tabby
Or if you wanna do a little bit of hard way, use Save Editor