IF it's a dragon fly nymph (can't look at the pic because of a slow connection) then I've found those in my mosquito-collection pans outside. (I leave standing water outside so that my fish can feast on them.)
I read somewhere that they will eat fry, but never heard of them attacking anything larger than fry...
I dropped them in my tank with the mosquito larvae and my guppies (young and old) tore them limb from limb and ate them. Quite entertaining actually, my guppies turned into pirahnas.
If you're still getting them in your tank, I have to assume that you don't have a top on it. Get a tighter-fitting lid so bugs can't lay eggs inside it.
I don't think eggs take very long to hatch, but if you raise the temperature they'll hatch faster.... So at least then you can be sure they're all hatched in a few days and watch them closely.
If you have any larger fish (over 4 inches, cichlids for example) I'm sure they'd love a protein-rich snack.
--- I just looked at the picture. Whoa! Those are nothing like the dragonfly babies I've seen.
Do you have any scaleless fish or inverts in your tank? If not, try something like ich-away or salt.
Multicellular parasites, insects, shrimp, crabs, etc are all fairly closely related- treatments for ich might get rid of the insects.
How big are they? In the pics they look a couple inches long... lol.You must have introduced the eggs somehow-
If you use rainwater, stop.
If you just bought some plants, let us know where. They might have hitchhiked in on plants.
If you used soil substrate or collected driftwood or something from a pond/river/anything else outside, now you know why not to.
I would probably raise the temp as I said, and just make them all hatch. They'll grow faster, be hungrier, but
at least in a couple days to a week you'll know they're all exterminated.
Looks kind of cool though- wish I had one.
I'd get a gallon jar and try to keep it or move it outside, but thats just me. I can't even squish bugs.