Depending of setting you have few choices:
1 - If the egg spawns on a bad place, just restart the mission. Example: Aurora near LZ is bad cause it is sorrounded by marauders at south and avengers at north, all other places are good and near e-fields
2 - You can avoid fighting the Elder (big blue bunny with powerful rockets). If you shoot the egg from the opposite side it will stand still, but if you active it you can fly around the egg to shoot always away of the big bunny. Run like hell if you make a mistake.
2 - Kill bunnies one by one. First the Breeder (medium sized red bunny). Better with a tank (so you can taunt it from safe distance). It is strong but not so much as the Elder, without rockets. Actually it is the support unit with repair target buff. Then taunt the Young bunny and finish it. You can switch to enginner for the rest of the task. With enginner you can kill the 1-2-3 packs easy. For the 4-5-6 packs you will need to run away with ab as soon as they spawn and kill them one by one. Note: 6-packs are actually the two 3-packs together, it happens. 4-packs spawn when you reach 50% damage, 5-packs at 75% (or 25% health).
Last note: the old tactics from past events doesn't work anymore, as the behaviour of the AI as been changed. No more "let-them-pod-me-and-stand-still" strategies.