You can use the 
Bribe special skill during the course of a battle to offer gil to an enemy. If you offer up enough gil, the enemy will flee the battle and will leave behind items for you.
Bribing enemies is pretty much a required mechanic for obtaining some of the items that you will need for crafting weapons and armor and for stat maxing your characters. Use this list below for more information on which fiends can be bribed.
Achievement/Trophy
You will receive the 
Under the Table Achievement/Trophy once you have paid for 100,000 gil worth of bribes.
Monster Arena
Note that fiends in the Monster Arena can be bribed just like a normal fiend out on the world map. There are no changes to the Bribe mechanics, so once you’ve captured a fiend and added it to the Monster Arena you can opt to fight it there and bribe it there to save you some time.
Bribe Mechanics
You will need to reach a certain gil amount in order to bribe an enemy, but even then, there is only a chance that the bribe will be successful. That said, once you have given enough gil to an enemy, adding any additional gil will stack on the previous gil that you gave it.
For example, if you bribe a fiend with 100,000 gil, and the bribe is not successful, bribe it with 1 gil on the next turn. This will count as a total bribe of 100,001 gil. As such, if the bribe is not successful, you should just continue bribing for 1 gil each time.
Full List
| Item | Fiends | Gil Needed |
|---|---|---|
 Al Bhed Potion |
Mech Defender Mech Gunner Mech Hunter |
174,000 56,000 110,000 |
 Amulet |
Tonberry | 270,000 |
 Arctic Wind |
Snow Flan White Element |
12,000 7,800 |
 Attribute Sphere |
Maelspike | 200,000 |
 Blk Magic Sphere |
Black Element | 152,000 |
| Bomb Core |
Bomb A Red Element |
17,000 9,000 |
 Chocobo Wing |
Machea | 360,000 |
| Dark Matter |
Land Worm | 1,600,000 |
| Designer Wallet |
Defender Z | 846,000 |
| Door to Tomorrow |
Mech Leader Mech Scouter |
74,000 55,000 |
| Dragon Scales |
Splasher | 4,000 |
| Dream Powder |
Bandersnatch Skoll |
36,000 20,000 |
| Elixir |
YKT-11 YKT-63 |
124,000 84,000 |
 Ether |
Guado Guard A YAT-97 YAT-99 |
40,000 74,000 54,000 |
| Farplane Wind |
Ahriman Epaaj Wraith |
56,000 174,000 444,440 |
| Fire Gem |
Bomb B Flame Flan |
44,000 30,000 |
 Friend Sphere |
Coeurl | 120,000 |
| Gambler’s Spirit |
Floating Death | 134,000 |
| Gold Hourglass |
Mushussu Nidhogg |
13,600 40,000 |
| Grenades |
Mech Guard | 25,600 |
| Healing Spring |
Achelous Octopus Phlegyas |
102,000 90,000 33,600 |
| Healing Water |
Anacondaur | 116,000 |
 Hi-Potions |
Dual Horn A | 37,500 |
| Hypello Potion |
Bunyip Mafdet Murussu Raldo Shred Swamp Mafdet |
8,000 14,200 11,600 4,800 39,000 17,000 |
| Ice Gem |
Ice Flan | 27,000 |
 Lv. 1 Key Sphere |
Imp | 17,600 |
| Lv. 2 Key Sphere |
Behemoth | 460,000 |
| Lv. 3 Key Sphere |
Demonolith | 900,000 |
| Lv. 4 Key Sphere |
Chimera Brain | 196,000 |
| Lightning Marbles |
Aerouge Gandarewa Gold Element Thunder Flan Yellow Element |
4,000 2,960 24,000 9,600 6,000 |
| Mana Tablet |
Chimera A | 105,000 |
| Mana Tonic |
Gemini (Blue) | 720,000 |
| Megalixirs |
Varuna Xiphos |
1,120,000 54,000 |
 Mega Phoenix |
Alcyone Ghost |
8,600 199,980 |
| Mega-Potion |
Dual Horn B Grendel |
75,900 190,000 |
| Musk |
Buer Evil Eye A Evil Eye B Floating Eye |
4,600 6,200 8,600 2,800 |
| Pendulum |
Master Tonberry Ultima Weapon |
960,000 1,400,000 |
| Petrify Grenade |
Basilisk Cave Iguion Dinonix Iguion Ipiria Melusine Raptor Yowie |
40,500 11,000 2,800 7,400 3,600 5,300 4,000 18,800 |
| Poison Fang |
Bite Bug Killer Bee Nebiros Wasp |
4,000 2,200 14,000 7,200 |
| Remedy |
Grat Lord Ochu Ochu Ragora Sandragora |
80,000 92,980 144,000 15,600 255,000 |
| Rename Card |
Zaurus | 157,000 |
| Return Sphere |
Dark Element Mandragora |
36,000 620,000 |
| Shining Gem |
Grenade Puroboros |
150,000 400,000 |
| Shining Thorn |
Larva | 29,960 |
| Silence Grenade |
Bat Eye | 7,600 |
| Silver Hourglass |
Kusariqqu Lamashtu Vouivre |
8,900 5,500 5,100 |
| Skill Sphere |
Zu | 360,000 |
| Sleeping Powder |
Dingo Garm Mi’ihen Fang Sand Wolf Snow Wolf |
2,500 4,800 3,200 9,000 8,000 |
| Smoke Bomb |
Condor Garuda C Simurgh |
1,900 80,000 4,000 |
| Special Sphere |
Adamantoise | 1,088,000 |
| Stamina Spring |
Bashura Ogre |
340,000 188,000 |
| Stamina Tablet |
Defender | 240,000 |
| Stamina Tonic |
Iron Giant Gemini (Red) |
72,000 720,000 |
| Supreme Gem |
Halma | 260,000 |
| Teleport Spheres |
Barbatos | 1,900,000 |
| Three Stars |
Behemoth King | 1,350,000 |
 Turbo Ether |
Funguar Thorn Exoray |
10,800 81,600 148,000 |
| Twin Stars |
Spirit | 200,000 |
| Underdog’s Secret |
Chimera B | 180,000 |
| Warp Sphere |
Master Coeurl | 260,000 |
| Water Gem |
Aqua Flan Blue Element Maze Larva Piranha Remora Sahagin B Sahagin C Water Flan |
40,500 30,000 44,440 1,000 60,000 27,600 7,600 6,300 |
| Wht Magic Sphere |
Dark Flan | 256,000 |
| Wings to Discovery |
Great Malboro Malboro |
1,280,000 540,000 |
| Winning Formula |
Sand Worm | 900,000 |
| X-Potion |
Guado Guardian C Valaha |
52,000 174,000 |