For the past few years working your "core" has been all the rage in the fitness industry, but few trainers nor the general population has any idea of what true core strength is or how to get it. *hint: Crunches will do nothing for you*
Building core strength and stability is often best addressed through static holds such as plank variations, woodchops, and other movements where one must contract not only the rectus abdominus (six pack muscles), but more importantly the external and internal obliques, and transverse abdominus - which are more important muscle concerning back health.
One sample progression is to move from static planks to dynamic planks. Then do them on a stability ball, then work up to hanging knee raises, then straight leg raises (hang from a pull-up bar and raise your legs into an L position), then hold the L position for time. Finally, try to do pull-ups while holding your legs straight out in the L position.
Then one day when you can do the following rope climb variation you'll know you've got not only some serious core strength, but a strong grip, back, and likely healthy shoulders.