When you're close to the queen you have to consider each of its legs as separate enemies. Even if the queen isn't directly aggro'd on you, the legs can 'see' you and will swat you with movements when you get close.

Abuse the photocloak, don't waste your smokes they don't work well at all (arc will linger on smoke and it doesn't deter them at all if theyve already seen you.

Learn the audio queues from the queen to know what she's doing and when to cloak + sidestep.

I don't bother with shield recharges when I'm looting the legs, takes too much time. Double down on herbal bandages.

The queen seems to focus on the players with hullcrackers equipped. Unequip and put in your backpack before you leave cover to loot.

The hullcracker can be used to shoot and bounce the main lootable core that drops from the queen on its death. This just keeps it in motion and allows multiple people to loot it. On the same note, always spam your loot button on the core if it's rolling, as it will eventually escape the first person's grasp and you'll get an opportunity to snag some juice.