I keep using Jalapenos and Ice shrooms to deal with the ice and fire balls but his R.V. keeps destroying my defence and the bungee zombies keep stealing my plants. Is there a recommended way to pass this level?
The trick to his level is to be conservative with your Jalapenos and Ice shrooms. They are NOT there to attack the boss, but rather to defend your plants. So let your other passively deal with the boss.
Always try to keep one flowerpot open per lane so you can use Jalapenos to take out Zambonis/Ice Balls, and alternatively to use Ice Shrooms to freeze their bungee zombies right before they pick up your plants(and of course destroy the fireballs, this will give your other plants time to attack them before any get stolen.
The R.V's are sadly nothing you can do about, only thing that counters it a little is to spread out your plants as much as possible but if you are doing this correctly this will become harder and harder so you will just have to accept your loses and rebuild on that point.