Syldra/Hydra Summon Location and Guide
Any time after you make it to World 3, return to Pirate's Cave to collect the Hydra/Syldra Summon. I typically wait until I get the Airship back before I come here but I'm fairly certain you can come here sooner if you want. Getting this summon is extremely straight forward, literally all you need to do is run into the room where you first got the boat/met Faris and Syldra.
Once you're in this area Faris will run over to the shore line and say that she thought she saw Syldra. A brief scene will commence that ends with Syldra becomming one of your Summons.
Note: In the PS1 version this summon is called Hydra, as you see in the screen shots below. This is because the Ps1 dub of the game is terrible and they can't even get Lenna's name right. The name of Faris' pet is Syldra which is the proper name of the summon, don't let the low quality Ps1 dub fool you!