In Brasilis, talk to Lucia (192, 133), who asks if you're here to hunt the Strange Hydra. If you want to, she will give you a Hydra Ball and tell you to use it one to capture it.
Note: You can obtain multiple Hydra Balls (saving time if the tame fails) by dropping any you have and talking to her again.
Find a Strange Hydra (located on the sand in Brasilis) and attempt to capture it with the Hydra Ball (the process is the same as taming a Cute Pet would be).
Once you succeed in capturing a Hydra, return it to Lucia. She rewards you with 3 Light Blue Potions, and gives you bonuses to DEX, LUK, and VIT for 20 minutes. She tells you to come back the next day to return another Hydra.