If you're like me, you played BioShock
on the XB360 and play it on Hard all the time. Thus, the newer difficulty offers an upgraded challenge to the seasoned players of Hard difficulty, and if you want to get the achievement by actually playing the game on this difficulty, here are some tips.
1: The biggest difference, as you no doubt imagine, is that enemies both deal and soak more damage. Otherwise, the rest of the game is largely the same. Resources are as abundant as they typically are, so it isn't as though you will be starved for bullets or cash.
2: The most effective Big Daddy killer on this difficulty is Security Bullseye: either by targeting the Big Daddy when it walks in front of a hacked camera, or deliberately triggering an alarm with a failed hack and then targeting it. Let the Security Bots do the work for you. It will save health, ammo, and EVE.
3: Keeping #2 above in mind, that's also the best and quickest method to research Big Daddies, Security Bots, and if they are present when you attack, Little Sisters. All of your shots will be Action Shots and if you frame them correctly, shots with Multiple Subjects.
4: On the topic of research, if you are patient, you can complete all research for the Nitro Splicer, Gun Splicer, and Little Sister in Neptune's Bounty, while also getting a pretty good jump on the research for Rosies, Spider Splicers, and the various Security devices. In addition to damage bonuses, this will also give you a handful of tonics that can be very helpful, particularly Photographer's Eye 2 for Level 2 Rosie research, Security Expert 2 for Level 2 Security Bot research, and Static Discharge 2 for Level 4 Gun Splicer research.
5: Before you go to the Smuggler's Den, take a detour and go back to Medical Pavilion. Fully research the Thuggish Splicer there (they are a bit tougher in Arcadia) and to get the Sport Boost tonics and the additional damage benefits. If you killed a Bouncer your first time here, take your *first* Bouncer photo on the Bouncer's corpse, since that will automatically push you into the next tier of research with the weakest possible photo. You can then photograph the living Bouncers in Medical for better bonuses. If you have not completed any Gun Splicer or Nitro Splicer research, you can also do that in Medical.
6: If you want more ADAM, take advantage of the Extra Little Sister Bug
. I can confirm that it works in this version of the game. The hardest one to take advantage of is the one in Arcadia as you have to be meticulous about triggering it, and you will not be able to use Security Bullseye to assist you. The easiest one to trigger is in Fort Frolic, so use it if you find yourself in need of additional upgrades. And since these trigger the rewards provided by Tenenbaum, if you are saving the Little Sisters, you will get the Tenenbaum rewards earlier in the game than you otherwise would. Again, this allows for quicker upgrades.
7: In the latter part of the game, the fully upgraded Chemical Thrower becomes potentially your best weapon. Combining Napalm with Human Inferno 1 and 2, or Electric Gel with Electric Flesh 1 and 2, on top of your research bonus, and Damage Research tonics 1 and 2, and most enemies go down very quickly.
8: Alternatively, the best weapon in the game can be the Wrench, but it requires Wrench Jockey 1 and 2, Wrench Lurker 1 and 2, the fourth Level of Bouncer Research, Damage Research 1 and 2, Frozen Field 1 and 2, Sport Boosts 1 & 2, and the all the other research bonus. It's a lot of combine, but it makes the Wrench capable of taking down Big Daddies.
9: The Fontaine fight can be finished without too much difficulty by equipping the following tonics: Human Inferno 1 & 2, Electric Flesh 1 & 2, Armored Shell 1 & 2, Eve Link 2, Sport Boost 1 & 2, Medical Expert 3, and then whatever else you feel will help you survive. Use the Chemical Thrower and Electric Gel for Rounds 1 and 2 of the fight. For round 3, use any remaining Electric Gel if you have it, and then switch to Napalm. NOTE: For rounds 2 and 3, as soon as Fontaine leaps out of the ADAM mechanism, hit him with the Security Bullseye. This will cause the Security Bots he summons at the start of those rounds to target him instead of you.
Hope this helps!