The Hyper Sting is a Lionfish and is present on many of Darius Games from Darius II to Super Darius II.
On this game, this boss is the easyest (due to the fact of be the very first boss). He only moves in circles, but advancing from one side to another of the screen. Like many other Darius bosses, his weak point is his mouth when open and it opens only for attacking, launching a laser straight ahead and some bullets to the Silver Hawk(s) current position. If you don't want to fight with him, you can use the smart bomb under him (shoot it when open) and kill him inmediately.
But...from behind appears another Hyper Sting. Don't worry, you can kill'em the same way as the first (including a second smart bomb)
Super Darius and Super Darius II
It fights and moves the same way as the original, but it stays on the left side of the screen and there is not another Hyper Sting comming from behind. The only thing that complicates this battle is the speed of lasers and bullets, Hyper Sting's size, no other weak points that makes easier the Silver Hawk movement and no smart bombs.
On Super Darius II, his weak point is his entire body (mainly his head). You can use the Super Darius II cheat for slow movement if don't want to lose your ships.