1.) Make sure you go into every gym battle 2-3 levels below your max level limit. You'll still be leveled higher than your opponent and this way you won't lose control of your pokemon during the battle.
2.) Don't be too focused on a core party. Often times your party from one gym to the next will look entirely different, and often times key additions to your party can be made in the areas made available to you right before the gym battle.
3.) Money and items are very plentiful in Reborn, don't be afraid to use them in a pinch. Revives can be found while mining and X items can be found littered across the map at every turn.
4.) The gym battles in Reborn are intended to be very difficult, more often than not you will have to attempt a gym more than once. Even if it's to see the opponents order and then reorder your own mons, don't expect to win the battle the first time.