This is one of the few easily-usable cards with destruction effects that work against "Stardust Dragon" and "Prime Material Dragon", since their effects only works against effects that are guaranteed to destroy a card.
If you have "Dark Armed Dragon" in your hand, use "Snipe Hunter's" effect to discard DARK monsters from your hand until you have the necessary number to summon "Dark Armed Dragon"; even if "Snipe Hunter's" effect fails multiple times in a row, you will still be able to summon "Dark Armed Dragon" and destroy the targeted cards anyway.
"Dark Armed Dragon" and "Snipe Hunter" continue to combo well even after "Dark Armed Dragon" is summoned, since neither have limits on how many times their effects can be used in a turn. Keep discarding DARK monsters in order to use "Snipe Hunter's" effect, then banish the DARK monsters from the graveyard to destroy more cards.
This card combo works well with an "Ojamasnipe" Deck: You first discard "Ojamagic" for "Summoner Monk's" effect to Special Summon "Snipe Hunter", and as "Ojamagic" is sent to the Graveyard (Provided that a card such as "Macro Cosmos" is not on the field), you receive 3 Ojama monsters listed on the card. You now have 3 chances to destroy up to 3 of your opponent's cards using "Snipe Hunter's" effect by discarding the "Ojama" cards.
This combo works even better if you discard a second "Ojamagic" for "Snipe Hunter's" effect.
"Thunder Dragon" can be used to produce more ammo for "Snipe Hunter". However, you can only discard "Thunder Dragon" as a cost to activate its own effect, not as a cost for "Snipe Hunter", or else "Thunder Dragon's" effect will not activate. You cannot share costs.
Another ammo would be "Volcanic Shell". Discard "Volcanic Shell" as a cost and pay 500 Life Points to get another "Volcanic Shell" into your hand, allowing you to destroy up to 3 cards.
During your Standby Phase, you can return "Sinister Serpent" back to your hand while it was in your Graveyard and discard it for "Snipe Hunter's" effect to have a chance to destroy 1 card your opponent controls. Then during your next Standby Phase, you may return "Sinister Serpent" back to your hand etc.