You will first encounter a Stingray on level 7 around halfway through. You don't need to kill the enemy just as soon as it appears on screen the achievement will pop. This is an unmissable achievement if you're playing through the game, but there are some ways to make the game easier.
Edit: Level 7 is the first level you can encounter them on, but they may first appear in later levels. Thanks to ShadowsofSatan for this!
EDIT: I don't know if the game changed since day of release but some people are saying level 8 is the first level they appear on. Maybe it was a glitch for me or something but I
got this achievement on level 7.
Before the game starts you can go into Settings
then Game Settings
and change your maximum amount of lives from 3 to 5. You can also turn on select level. This will allow you to choose any level that you have reached. I would also recommend holding down the
button instead of pressing the
button because it shoots faster.