ZvT How to beat mass battleships?

1v1 game in the Bronze league. I scouted the Fusion Core early and knew Battleships were coming. My plan was to use Hydralisks to counter, but I still lost. I did manage to kill 2 expansions with my ground force, but still felt that I had no chance throughout the game.
What did I do wrong?

Replay: drop.sc/replay/24750281

Get spire ASAP and morph corruptors. Hydras are good vs BCs only with certain proportions. Corruptors are zerg strongest anti-air units. Also if you have enough APM (i know, you’re bronze) you can get infestors and completely obliterate battle cruisers by neuraling them and then using their own yamato to kill them. Takes couple of practice but if you learn it BCs will no longer be an issue to you. Good luck.

Don’t forget your upgrades once u hit 3/3 takes two corrupters to destroy bc but with Yamato you need 3