Gun N Run is world style in N Terraria. Like Dungeon, Gun N Run has score, which, in death or leaving the world will provide you coins and exp.
Gun N Run don't have similar health system than other worlds. You start with two hearts, that block you from death. You don't want to take the damage, 'cause every damage will kill you. After hearts are gone, taking damage will kill you, and you respawn as ghost. Hearts can be collected from enemies.
Weapons and damage
You can use only guns. You start with Flintlock Pistol, and you find other guns from enemies. Every gun make one damage, but enemy health are so small, that you don't even have to care it! For example, Zombies health is 2-3, depending what kind of Zombie, but Green Slime Have only one health! Of course, there are exceptions about damage, some guns make more damage!
Fighting against bosses
Like in every world, you can fight bosses, although your inventory in Gun N Run is only your gun. Summoning bosses in Gun N Run is to kill certain enemies. For example, kill Demon Eyes to summon Eye of Cthulhu. Because you don't have pickaxe, you always have in Gun N Run world a way to Underworld.