Prepare an ice-water bath. In a large pot of boiling water, cook the shrimp just until the flesh is opaque, about 3 minutes. Drain the shrimp and place in the ice-water bath. When cool, immediately drain well and pat dry with paper towels.

Cut the avocado in half lengthwise and remove the pit. Use a sharp knife to score the avocado flesh into a small dice and then scoop it out with a spoon into a large bowl.

Cut off the ends of the grapefruits and place them on a cutting board, standing each on its flat side. Remove the peel with a knife, making sure to cut all the way at the pith, exposing the pink flesh. With a sharp knife, remove segments by carefully cutting on each side of the membrane. Place in the bowl with the avocado.

Add the shrimp, mango, tarragon, and cilantro to the bowl. Toss with 1/4 cup of the lemon vinaigrette, season with salt, pepper, and the lemon juice, and toss again.

Toss the greens without the remaining 1/4 cup of vinaigrette, add to the shrimp mixture, and gently toss together. Divide among four chilled plates and serve.