Well, if you didn't already, you can craft the magic map. That will help a lot, since it will show the Hydra Lair before it's even in your FOV, because of the large area the Magic Map shows. Twilight Streams border many different biomes and as such are good ways of reaching the biome where Hydra's usually spawns, Swamp & Fire Swamps.
Other than that, it always helps to have some sort of enhanced mobility whilst scouting out the twilight forest, preferably flight, since that lets you bypass most of the difficult terrain that sometimes makes moving around difficult. Jetpacks, Advanced Jetpacks or Gravisuite, depending on how many resources you currently have. If you don't want to use tech, or don't have money to get tech, the Boots of the Traveller are pretty cheap to make and easy enough to research, and they enhance mobility by quite a bit. But then again, you don't want to fight the Hydra unless you have at least a full set of Diamond Armor, preferably enchanted, and a potion of regeneration wouldn't be a bad idea either. To actually damage it, ranged weapons are much better than melee. Mining Laser/Lightning Wand both are tied as the top tier ranged weapon for this fight, but Xeno's Reliquary Handgun is also pretty good, but surpassed by a bow with a good enchant. Fire will do nothing for you here, so no fire aspect swords or fiery bows. Wait for the Hydra to open it's mouth before shooting it to deal maximum damage.