Hydran Stingers are dangerous, and you should use maneuvers to avoid letting them get close. Keep your speed at 16 (with a few acceleration points) and stay ahead of the fighters.
Never engage the fighters and the ship at the same time, and if he tries to get his ship close before launching, stay away from him (to avoid playing to his strength). Stingers are expensive, and either you have a much bigger ship or you have more ships than he has. So before his fighters launch, you outnumber and outgun the Hydran. Use that to your advantage!
If the fighters are deployed, fire phasers and disruptors at the fighters at Range Five, and either save some for your alpha strike for his ship or use all your weapons on the fighters and stay away from his ship! After the fighters are destroyed, you can rearm and then go ship-to-ship with an outnumbered enemy.
If he keeps the fighters on board and tries to close, stay away from him, but pound him with whatever weapons you can bring to bear without going head-to-head (which lets him get close and I told you not to allow that). If you get close to a Hydran ship, go in on the oblique (his ship should be to one side of straight ahead) so that he cannot use all of his gatlings on the same impulse, and then use all of your weapons (phasers, disruptors, and an offensive burst of ESG) and target his weapons. At Range 1, two ESGs will do as much damage as four overloaded disruptors without the die roll (but using more power). If he fires his hellbores, take the damage and tractor him, to allow you to use your ESGs on him again next turn while his Hellbores are rearming. You can do a second full alpha strike next turn; he cannot.
Against Kzintis (or WYNs), go straight at him on the first turn to avoid letting him build up a drone wave. Approach obliquely to avoid his centerline firepower. (LS and RS weapons fire straight ahead.) Use phaser-3s to take down the drones, and then offensive burst your ESGs at full power. Target weapons as this will cut down on his drone throw weight. You're going to take some damage in any head-on pass, but you can give better than you get and absorb punishment better. Tractor him so you can repeat your attack next turn, and put enough into tractors to hold him and then spend the rest on weapons. You're already close to the Kzinti and you don't need to move. If Mister Kzinti stays away, fire every turn (in overload range) as you will have more phaser-1s in arc than he does (if you avoid his centerline like I told you to). Build up power in your ESGs which have no holding cost and overrun him at speed 24 when the ESGs are full.