It's really quite easy once you know how to approach it:
1. Don't use your dragon breath at all.
2. Use the fire sphere to take out ballistas from a distance (takes 2 hits).
3. Summon the wyvern near nests to distract enemies.
4. Use the special ability on the islands with big clusters of enemies, like the ones with nests or lightning towers surrounded by ballistas. Fire it right in the middle and it'll take out most of them in a big radius. Save for only these big groups as it has a long cool down.
5. Stay pretty far ahead of the zeppelin clearing the way but close enough that you can use the zeppelin targeting skill to help you take out nests. Also let it handle the flying stragglers on its own and you deal with the big stuff.
By the end of it the zeppelin should be no lower than like 95% health if you do it right.
