“a stronger core”
Core means the center, but in exercise it refers to the muscles in the middle of the body, such as the abdominal and back muscles. Not just bigger arms means not only bigger arms. The trainer recommends training the core as well, instead of focusing only on the arms.
“improves your posture”
Posture means the way you hold your body. The trainer explains that a stronger core improves posture and consequently how Tina looks in photos.
“Should I do more cardio”
Cardio shortens cardiovascular exercise and means aerobic activities such as jogging or cycling. Gyms often contrast cardio with weights, or strength training.
“Stick with the plan”
Stick with something means to continue it without giving up. Stick with the plan asks Tina to keep following the training program.
“My poses will.”
My poses will. is short for My poses will change every day., picking up the trainer's previous line. The trainer has said that even if Tina takes a photo every day, her body will not look different every day. The punchline is Tina's comeback: but her poses can change every day. She is more excited about changes in her photos than changes in her body.