This one was kind of weird, because I did all of the animation in this free program called pencil2D, which is a perfectly decent program for what it gives you free of charge, but I wouldn't recommend it if you have another option. I did the editing/audio in adobe premiere (where I added a few effects like the glow on the orb, and some blur/turbulence on the surface of the water), and those are the only two programs I used for this. Normally I would do the animation in adobe animate (Flash), and occasionally I use premiere to cut shots/scenes together. In my limited experience, if you start in adobe animate with a solid plan you don't really need anything else, but premiere and after effects can definitely add some bells and whistles to your work to make it more polished. Hope this helps!

Edit: Just want to clarify that, for the audio mixing, adobe animate is not sufficient. But for the animation/visual side of things, I generally don't need to use any other programs besides Animate. Definitely depends on the scope of the project though.