Minecraft wiki entry for Hardcore_mode, associated text: Anywhere between 32 and 64 arrows, unless using an Infinity bow, then only one arrow is needed.
At least 4 stacks of food, preferably steak or cooked porkchops. Golden carrots are even better, but more expensive.
A few stacks of obsidian, to use for building. This can also be used to block explosions when she is perched and you use beds.
Two water buckets to distract endermen. Water buckets can also be used to break a fall in a pinch.
At least one enchanted golden apple. If you have more, do not hesitate to bring them. Remember, you can only respawn in spectator mode
Potions of regeneration, about four of each type:
Extended potions of regeneration. Should be active after taking damage, if not slightly beforehand.
Splash potions of regeneration II, for quick healing.
Potions of Strength. If inventory space is not a problem use tier II potions. Take two extended potions or six tier II ones.
Splash potions of healing II. If melons are available, fill all remaining inventory space with splash potions of healing. Before entering the End, learn to differ them from regeneration potions.
At least one spare ender pearl to teleport to the land, in case your spawnpoint is above the void. You can get easily knocked off by the dragon in the first few seconds, much before you can build yourself to safer ground. They are useful to avoid fall damage (or falling into the void) if the dragon throws you high into the air. They are also useful to reach the outer islands without going back to the Overworld after killing the ender dragon, but endermen in the End are a convenient source of them after the dragon is dead.
At least 3 extended slow falling potions. Apply slow falling before the fight, and apply it during the fight if it wears off. The ender dragon's attacks inflict a heavy amount of knockback, flinging players high up into the air or off the island. Slow falling will negate the effects of fall damage, allowing you to fall back down safely. If you get knocked off the island, slow falling can be used to glide back to the island.
A carved pumpkin, since endermen will not turn hostile if you are wearing one. Switching to third-person point of view will remove the obstructed vision carved pumpkins cause when worn. Beware that when wearing a carved pumpkin instead of a helmet, you will have less armor points and will not be affected by any enchantments on the helmet.
A spyglass. The spyglass will be useful for tracking the dragon's location and you can also use it to zoom in on the crystals you have not broken.
Some flint, sticks, and feathers, in case you are not using an infinity bow and happen to run out of arrows.
A Totem of Undying, it can help you a LOT.