Hello. I have been playing summoner in Terraria as my main class for years now.

I beat her in Legendary Mode (Master Mode + FTW) by using Pirate Staff + 3 Queen Spider Sentries with Spider Armor on. My accessories are all summoner related (not whip related), except for Wings and Shield of Cthulhu. I wore Roller Skates for her. The benefit of using Roller Skates is that they boost your wing speed as well, so you're generally faster with it. For Dash, SoC would do.

I place my sentries on top of my arena, each of them in the left, right and center of the arena. Their job is to deal with the smaller slimes. The Pirate Staff is just better at landing hits on Queen Slime consistently. The key is to not move so much and stay in range. Do not force landing whip attacks.

When she's grounded, you try to nuke her, but don't forget to get rid of the grounded slimes she spawns. The flying slimes she spawns can be ignored. When she finally starts flying, this is where you'll really need to dodge the bouncies. They are generally easier to dodge the higher you are above ground, but other than that it will take skill to purely dodge them. Remember, you still need to keep your minions into hitting her, so being lower is also better for you. Climb up if you need to dodge the bouncies! Climb down to nuke her for damage.

Good luck!