Have you ever tried an overhead squat?
It may seem odd to associate an exercise known for building your legs as a "core exercise," but give it a shot and watch your technique, making sure to keep your weight over the arches of your feet and your arms straight overhead.
If you felt your weight shift back onto your heels or forward onto your toes, or if you noticed your knees collapse inward or your arms move forward, then you can stand to improve your mobility, stability and overall "pillar strength."
Your pillar encompasses muscles from your hips to your shoulders, including your torso, so performing pillar-strengthening moves will engage your abs and back while building stability around your hips and shoulders.
Doing squats alone isn't enough, and it doesn't replace traditional abdominal and core exercises like bridges. But the squat is a great indicator of strength and stability, and it will make you stronger. Which is why it should be a staple in your training program. A proper squat requires tremendous coordination of joints, balance, stability, and strength. You should feel tension throughout your abs (but still be able to breathe comfortably) if you're doing it right.
Try many variations of squats, including the overhead squat, single-leg squats and split-stance squats. Here's a video.