Minecraft wiki entry for Hardcore_mode, associated text: Always watch your back. Some of the most common deaths are from a creeper or a ghast, both of which can't be ranged by sound. The fastest way a creeper can get to you is dropping from above.
Fall damage is a common way of dying, so wearing boots with Feather Falling IV can be very helpful as you will be very unlikely to die of fall damage unless your health is low.
Never attack two creepers in a row or at once. The same goes for skeletons because their long-range shooting means it's hard to get in close.
Shields are inexpensive to make, but can save your life if you get trapped with a creeper or skeleton.
Never take unnecessary risks. Sometimes there are necessary risks, but most things probably are not worth the chance of death or losing a lot of health that may lead to death. For example, in most situations, it's better to bridge a gap over a lava ocean to a Nether Fortress than to throw an ender pearl to get over there.
Mobile inventory space can be increased through the use of ender chests, shulker boxes, horses, donkeys, mules, and llamas with a chest.
Don't be afraid to place plenty of torches all over the ground. Surviving is easier in a well-lit area.
Beds are critical, especially early game. They bypass monsters spawning at night (and prevent phantoms). This is very helpful for exploring the surface and gathering basic resources in safety. To save materials, break and reuse the same bed. Normally breaking a bed is a bad idea(as the player will spawn in the world spawn if you die), but in hardcore mode, you will not respawn.
Avoid going out at night until you're well prepared, with iron or diamond equipment, and preferably a safe zone to retreat to. If night suddenly falls upon you, retreat to a shelter (if one is close enough), or build one. Even a simple pillar is helpful for surviving the night.
Avoid dangerous areas early in the game such as caves and ravines. It's best to stay away until you are better equipped with iron armor and tools.
Wear your best set of armor at all times, replacing it as it gets worn. (You can also enchant your armor with Mending so it can always be repairable.) Remember that unenchanted armor doesn't protect you against falling damage, Poison, Hunger, etc.
Avoid lags and don't use glitches. You won't want to have your computer lag for an hour and then find out that you died when the lag was occurring.
Sometimes it's better to flee than fight. Always have a solid block on your hotbar and practice key binding so you can build a barricade and shelter on short notice.
Try to keep your hunger meter full at all times - regenerating health might save your life and eating in the middle of combat can be hard to do. Remember: hunger can kill you.