What are some good ways to make character movements look smoother and more natural in Adobe Animate?

The perception of smoothness in animation comes from the correct application of various fundamental principles, such as anticipation, overshoots, follow through and layering secondary actions on top of the primary ones.

Movement along arcs is extremely important as well as proper easing which choreographs the flow and accentuates the important poses.

Using digital cutouts and classic tweens lets you experiment and polish animation relatively quickly, as long as you stay focused on the posing, timing and spacing of your keys and don’t let the medium dictate it all. The most common issues with tweened animation are melting of form, disjointedness and floatiness of movements. Those are easily avoided when the animator has a clear vision what good animation should look like.

I’d focus on timing and spacing first, then use easing and a few well-placed keyframes to make the movement feel more natural.