Not a fix for the battery, but if you're on Android, enable developer settings and change your animations to 0.5x speed (there are three settings to change). Every OS animation will take half as long. It makes an aging phone feel much snappier.
That really did make using my old phone less painful, thanks for the tip!
Won't 0.5x speed make it slower (Driving 20mph instead of 40mph will get you somewhere in double the time).
I just checked my phone, the phrasing is "Animation scale .5x" (Among other numbers), meaning it's scaled to take n times the time.