Yes they can destroy missiles.
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No.
you nuke with nuclear fission and fusion
Ten Tactical Nukes to unlock the emblem.
There are many ways to kill characters on Fallout 3: Shooting Grenade Mines Missiles Mister Sandman perk (level 18 perk, useful in Rivet City when you want to dominate the town) Mini Nukes (350 per nuke) Endless ways.... use the way that works for you! Hope these options help :)
i'd say you will have to get 10 nukes because my friend had 9 nukes then got another in a match and at the end of the game in the lobby he had earned the nuke emblem! So I really hoped this helped you to try hard to get a nuke!