BioShock Infinite

1999 Mode is the hardest difficulty in the game. Not only do enemies have a lot more health, but they do a lot more damage to you. There is no Aim Assist and ammo is in less frequent supply, meaning you have to carefully manage your weapons and Vigors to gain as much of an advantage as you can. Your objective marker is also removed, so you really have to know your way around the map and exactly where you’re going. To compound your woes, you are not allowed to purchase anything from a “Dollar Bill” vending machine. You can, however, buy upgrades from “Minuteman’s Armoury” and “Veni Vidi Vigor” machines. If you accidentally access the "Dollar Bill" machine, do not worry as only actually buying something from it will lock you out of this trophy.

Just like in the other difficulties, you will be revived when you die. However, in 1999 Mode it costs $100 per respawn, and if you run out of money you will be sent to the Main Menu and you will have to reload your save from the beginning of the last Chapter. There is an exploit for this if you have no money however, which is to pause the game when you die and choose “Reload Checkpoint” from the menu. This will set you back to your last autosave, which are far more frequent checkpoints than the beginning of Chapters.

Tips and Strategies:

• The first and most important thing you should remember is patience. If you run headlong into a fight, you're going to have a bad time. You will die extremely quickly if outnumbered, so hang back and try pick enemies off. Use cover as much as possible, either using the environment or the specific Tears labelled "Cover".
• Following on from this, the Sniper Rifle is your best friend. Always have it with you as your primary weapon and upgrade it as quickly as possible. This way, you can stay out of the heat of battle and pick enemies off from a distance. If you take damage, take cover until your shield regenerates before popping out again.
• Your secondary weapon should either be the Shotgun or the Hand Cannon (depending on their availability and the amount of ammo you have, or just your personal preference), so upgrade these next. The Volley Gun is also useful as it does a lot of damage and has more range than Shotgun and Hand Cannon. When fully upgraded, headshots are one-shot kills on normal enemies even on 1999 Mode and do significant damage to the more powerful enemies if combined with Shock Jockey for the "1-2 Punch". Weapons such as the Pistol and Machine Gun are useless in this mode. Even if upgraded with damage and ammo capacity upgrades, you will expend most of your clip taking down just a couple of enemies.
• The Possession Vigor is absolutely vital. Make sure that this is the first one you fully upgrade. Every time you are about to fight, scout the area for any turrets or machines you can Possess to greatly help you thin out the enemies. Also use it immediately on any heavily armoured or RPG enemies as they will distract enemies, allowing you pick them off with you sniper. They will then commit suicide once the effect wears off, meaning you don't have to deal with them yourself. Using Possession on Patriots not only turns them on other enemies, but makes them turn around and expose the weak point on their backs, allowing for a much easier kill. Possessing vending machines will also give you as much as $40 (but only once), which is useful for buying upgrades.
• Other Vigors are good for certain situations. The secondary Vigor I used the most was Bucking Bronco. Even the vanilla version hits multiple enemies at once and throws them in the air (meaning you can do significantly more damage with your weapons), whereas Shock Jockey and Devil's Kiss only affect individual enemies unless powered up wth expensive upgrades. Murder of Crows is great for staggering multiple enemies at once, giving you an opportunity to take them out or run into cover and recover your shield. Undertow is an excellent Vigor to use when outside, as you can push many enemies off the edges of Columbia and conserve ammo. Return to Sender is particularly useful for enemies with a lot of firepower such as Patriots. You can absorb a lot of bullets before unleashing it back on them to deal considerable damage.
• Collect as many Infusions as you can during your playthrough. Use the guide listed under the Infused with Greatness trophy description for locations. If you have bought the Season Pass, the "Early Bird DLC pack" will greatly help you wth this as it will give you 5 Infusions from the start when you pick them up in the Blue Ribbon Restaurant. I recommend fully upgrading health first with perhaps one or two Salt upgrades thrown in, before focusing on Salts second and finally Shield.
• You don't always have to fight! Many battles can be skipped by running past the enemy and opening a door or activating a switch. Of particular note is that only the second Handyman fight is unavoidable, the other three can be skipped by quickly rushing to the next area.
• Elizabeth isn't just your AI partner; she is also incredibly useful. During fights, if you are running low she will provide you with health packs, Salts and ammo. When the prompt appears, press to catch the items she throws at you. You are also invincible when this animation is playing.
• Loot everything you come across. The money you earn from this will be invaluable, as will the ammo. If you know you are about to enter a fight and you are near max health or Salts, don't pick up health packs or Salt bottles in containers just for the sake of it. Be smart and memorise where the container is, and during the fight head back there for the resource if you are running low.
• The absolute best piece of Gear is "Winter Shield". This gives you 10 seconds of invincibility every time you jump on and off a Sky-Line or freight hook without any form of cooldown. This makes every outdoor fight where there is a Sky-Line (such as all of the Handyman fights) a breeze. Coupled with Fire Bird (fire damage to all enemies within a small radius of your landing point), you can just keep jumping to a Sky-Line and attacking each individual enemy with Sky-Line Strikes at the cost of no ammo and no health loss.
• A great piece of Gear for indoor battles is "Blood To Salt", which gives you a 40% chance of automatically receiving Salt packs when you kill an enemy. This is particularly useful for players who tend to use Vigors more than weapons.
• Unfortunately, each piece of Gear is random. Therefore, you may get the ones mentioned above right at the start of the game, near the end, or not at all. However, there is a workaround. When you find a piece of Gear and it is not to your liking, pause the game and restart the checkpoint. Find the piece of Gear again and it will be something completely different. Do this as many times as required until you get the one you want.
• If you are struggling on any particular section, you may want to check out this thread which contains a wide variety of tips from different players: The Official 1999 Mode Progress/Help Thread

Infinite money and lockpicks exploit:

You can farm unlimited money and lockpicks in Chapter 12: "Return to Hall of Heroes Plaza". This is immediately after exiting the Hall of Heroes. Farming lockpicks will come in handy when going for all of the collectables as some collectables are behind locked doors that require lockpicks to open. The maxiumum amount of lockpicks you can carry is 30, which is more than enough to open all the locks from this point in the game onwards.

The money farming can be a big help on your 1999 Mode playthrough, as you get a random amount of money (anywhere between $10 and $40) everytime you possess this particular machine. You can use the money to first upgrade the weapons and Vigors you want, and after that, you can use the money to cover the $100 cost of your deaths. Farming the money does take some time, but if you farm this for an hour or two, you will have thousands of coins to have as back-up for when you die.

For the farming method, follow the steps below:
1) Possess the Dollar Bill vending machine on the left side, after leaving the Hall of Heroes.
2) Use the Sky-Line on the right-hand side until you come to a platform. There are some enemies on the platform. Jump down and pick up the lockpick. It's on a wooden plank under the stairs.
3) Return to the Hall of Heroes, refill your Salts with the Salt machine if needed (can be refilled unlimited times).
4) Go back outside and repeat what you did earlier. The machine can be possessed again and the lockpicks respawn.

If you kill the enemies in front of the Hall of Heroes, they won't respawn. So you can keep farming without having any trouble with them.

Here is a video walkthrough explaining this method (thanks PowerPyx):

Note: This exploit has been patched somewhat. You can still repeatedly farm the vending machine for coins, but you'll only get around 500 per hour as opposed to the thousands you used to get. It probably isn't worth farming now, as you should have more than enough money to get through 1999 if you consistently loot and search everywhere. It is handy, however, to max out on lockpicks.

Of course, if you delete your game data and decline the numerous patches, this method will still work.