The 53 TONICS are obtained from finding them, researching subjects with the camera, saving Little Sisters, inventing them at U-Invent machines, and purchasing them with ADAM at the Gatherer’s Garden. Tonics obtained in this way count towards the 53 that you need for the achievement. All of the new ones from the DLC cost one ADAM.
With this in mind, you must SAVE ALL little sisters and I recommend not killing Cohen until you find him at Olympus Heights as he gives you a tonic for free (you can buy it later) and there are achievements related to him.
IMPORTANT NOTE: The Tonics you buy for 1 Adam (from the free DLC) DO COUNT towards this achievement, as I got it before getting all the normal tonics. The following are the tonics from the DLC:
EVE saver (use less EVE for plasmids),
Vending Expert (reduce vending machine prices), and
Machine Buster (increases damage to...well, machines).
Here is the complete list of tonics (DLC not included):
Tonics (53 Total)
Physical Tonics (19)
1. BloodLust - U-Invent machine / Inventable after Arcadia
2. Booze Hound - U-Invent MAchine / Inventable after Arcadia
3. Eve Link - Sold at Gatherer's Garden machines
4. Eve Link 2 - Farmer's Market / On the ground near U-Invent & vending machines.
5. Extra Nutrition - Sold at Gatherer's Garden machines.
6. Extra Nutrition 2 - Storage Basement of the mall area in Fort Frolic. Covered by metal grate if Cohen dies. Also purchasable.
7. Extra Nutrition 3 - Research Spider splicers
8. Hacker's Delight - Cremate the body in the Medical Pavillion.
9. Hacker's Delight 2 - U-Invent machine / Inventable after Arcadia
10. Hacker's Delight 3 - Proving Grounds / Same room as the Big Daddy Helmet.
11. Medical Expert - Neptune's Bounty / In the center of the muddy section of the Lower Wharf.
12. Medical Expert 2 - Fort Frolic / Awarded by an alive Cohen or bought in Hephestus
13. Medical Expert 3 - Near the toilets in Dr. Suchong's Clinic on the second floor of Artemis Suites.
14. Natural Camoflouge - Research the Houdini Splicers
15. Scrounger - Research Leadhead splicers
16. Security Evasion - Arcadia / In the center of a group of splicers, near an Invent machine.
17. Security Evasion 2 - Hephaestus / Heat Monitoring / Across from electricuted ghost scene, sitting on desk
18. Sportboost - Research Thuggish splicers
19. Sportboost 2 - Research Thuggish Splicers
Engineering Tonics (16)
1. Alarm Expert - Fort Frolic / Theater / Top Left balcony sitting on the ledge
2. Alarm Expert 2 - Point Prometheus / Optimized Eugenics / on filing cabinet
3. Clever Inventor - Suchong's Apartment / Beside the tape recorder
4. Focused Hacker - Neptune's Bounty / In the area right before fighting Peach Wilkins.
5. Focused Hacker 2 - Hestia Fourth Floor, on the desk in the corner of the room near the safe.
6. Hacking Expert - Arcadia / Sitting on the first desk in Langford Labs
7. Hacking Expert 2 - Available in Gatherer's Garden vending machine, starting in the Fort Frolic area.
8. Prolific Inventor - Awarded for saving Little Sisters / Last Tonic reward
9. Safecracker - Awarded for saving Little Sisters / First Tonic reward
10. Safecracker 2 - In the Autopsy room in the downstairs of the Little Wonders Educational Facility.
11. Security Expert - Medical Pavilion / On a small chest in the morgue.
12. Security Expert 2 - Research the flying Security Bot
13. Shorten Alarms - Neptune's bounty / Near "Saw Masha Today" recording or buy it at a Gatherer's Garden machine in Arcadia.
14. Shorten Alarms 2 - Hephaestus / On the floor right before setting off the EMP.
15. Speedy Hacker - Medical Pavilion / On the desk in the dentist's lab.
16. Speedy Hacker 2 - Available at Gatherer's Garden vending machines, starting in the Olympus Heights area.
Combat Tonics (18)
1. Armored Shell - Available at Gatherer's Garden vending machine, starting with the Medical Pavilion area.
2. Armored Shell 2 - Awarded for saving Little Sisters / Second Tonic Reward
3. Damage Research - Hephaestus / Across from the EMP bomb on a table
4. Damage Research 2 - In the Mendel Family Library, on a desk in the rear of the room.
5. Electric Flesh - Fort Frolic / The Projector Room in the Theater / On bookshelf
6. Electric Flesh 2 - Olympic Heights / Fontaine's apartment / In the office on the desk
7. Frozen Field - Fort Frolic / Awarded for killing the Cohen victim in the freezer
8. Frozen Field 2 - Hephaestus - Room off entrance to Ryan's office - on desk
9. Human Inferno - Arcadia Gatherer's Garden machine / 20 Adam
10. Human Inferno 2 - Available at Gatherer's Garden vending machine starting in the Point Prometheus area.
11. Photographer's Eye - In the bunk room of the wine cellar in Farmer's Market.
12. Photographer's Eye 2 - Research the Rosie Big Daddy.
13. Static Discarge - Medicial Pavilion / In the hallway after fighting Steinman.
14. Static Discharge 2 - Research Leadhead splicers
15. Wrench Jockey - Medical Pavilion / Seen from a window. In a back room, reached by airshaft.
16. Wrench Jockey 2 - Research Bouncer Big Daddy
17. Wrench Lurker - Neptune's Bounty / Sitting on the ledge near the plasmid machine.
18. Wrench Lurker 2 - Available at Gatherer's Garden vending machine, starting at Olympus Heights.