It's hard to know exactly what they do on the show because they edit it so much. Suffice it to say they take a total body approach doing everything from weights to boxing and a lot of medicine ball work. I'm a proponent of free weights and dumb bells over machines because machines tend to isolate and using dumb bells gets more parts of your body involved.

Here's a few exercises that will help you get the arms and shoulders like Alli.

Bench press (8 reps x 3 sets)
Incline Dumbbell Press (8 reps x 3 sets)

Military Press
Lateral Raises

Dips (as many as possible)
Tricep Extensions

Lat pull downs (8 reps x 3 sets)
Barbell Rows (8 reps x 3 sets)
Deadlifts (8 reps x 3 sets)
Dumbbell Shrugs (hold at the top for 2 seconds)

Barbell Curls (8 reps x 3 sets)
Dumbbell Curls (8 reps x 3 sets)

Wrist Curls (12 resp x 3 sets)