Big Game Hunting

I've reached a point where I can always kill Adamantoise without the Death Spell. Killing them with my weapons is far more satisfying. Problem is, I still seem unable to kill them without first knocking out their legs with my summon. This isn't really that big of a problem, however my Platinum Ingot and Trapezohedron harvesting would go much faster if I didn't constantly have to seek out lesser creatures to slaughter to rebuild my TP between giant turtles. Does anyone have any good strategies for them? Paradigm decks, accessories I may be neglecting? My primary party is Fang, Lightning & Vanille. Crystarium is maxed out for all.

Fang, Vanille and Snow make a far more excellent team than Fang-Lightning-Vanille, I recommend using them ;)

Paradigm Deck (order is Fang, Vanille, Snow):
1. SYN/COM/RAV
2. RAV/RAV/RAV
3. COM/MED/MED
4. SYN/SAB/SAB
5. COM/COM/SAB

Equipment:
Fang
- any weapon, except Taming Pole, Stagger Lock isn't cool (Dragon Horn is the best IMO, cause it has a great Strength value)
- Genji Glove
- 2x Power Glove (it is good if they are maxed, but you should have at least 2550 strenght)
- Gaian Ring (maxed for better defense)

Vanille
- Marlboro Wand
- Connoisseur Catalog
- Collector Catalog
- Sprint Shoes
- Gaian Ring (maxed for better defense)

Snow
- Soul Blazer (maxing it is not essential, but can help you)
- Weirding Glyph
- Gaian Ring
- Sprint Shoes
- Growth Egg (if you need more CP, otherwise equip some Magic bonus stuff)

Strategy
Start with Paradigm #1. Fang is a SYN in this paradigm, so cast Bravery and Haste on her. Then quickly switch to Paradigm #2, attack its leg until stagger (keep attacking it until the chain gauge is on approximately 500%), repeat it with the other leg. Then switch to Paradigm #3, and Highwind the first leg and right after the second leg
(Note: if you are not quick enough, try staggering the first leg and right after switching to Paradigm #3, do Highwind, then switch back to #2 and do it with the other leg, but in most cases, you can get both leg staggered and have enough time to do Highwind).
As Fang has enough Strength to knock the legs, poor little turtle will be sleeping on the ground. With Paradigm #4, recast Bravery and Haste on Fang, and cast Faith and Haste on Vanille and Snow. When you're done, Vanille and Snow have already debuffed poor little Turtle. Make sure it has Imperil, Deprotect, Defaith and Slow on. When all of them are on, switch to Paradigm #2 and bring up the chain gauge with some magic power, until you see it staggered. Then switch to Paradigm #5, and attack it. Fang has a high physical damage-dealing potential, Snow's Daze shake the crap out of the turtle and Vanille... well, she can assist you and deal a little damage. You can activate Highwind when the turtle's life is near the first quarter, but if you have a fully expanded Crystarium and have the mentioned equipment, you can kill it without Highwind (my best time is 1:11 with this tactic, the average is 1:30-2:00)
I maxed my Crystarium with this strategy, also got 60 Plat. Ingots and 11 Traps, and finally got my Platinum Trophy under 85 hours of playing the game.
Oh, and I recommend you the Archelyte Steppe route to farm these poor little turtles! Activate Mission 63 in Sulyya Springs, teleport back to Archelyte Steppe, Northern Highplains, ride the chocobo to the canyon where the mission mark is. Here you can find 3 turtles, 2 more are walking not so far from here, so you can kill 5 in one turn. I think the drops are better if the mentioned mission is active, at least I got all my Traps here and not a single one in Eden. Enjoy your farming ;)

Note 2: don't get sad if you got no Traps during your first turns... I was quite disappointed that I only got Plats in the first three or four turns, but after that I got 5 Traps in a row. It's just a matter of luck, keep trying :)

Thank you, Cortez. My own strategy didn't need too much modification. What I lacked was the Gaian Rings. Now that I have them, I can consistantly slay the Adamantoise without summoning Bahamut. I stuck with Lightning, as she's better than Snow at everything except Sentinel, and if I'm not using a Sentinel, no need to bring him in. I did have to give up Vanille's Random Instant Chain ability for this, but not Lightning's, so she's still able to just randomly instant chain the legs while I'm casting my buffs. Huge help.

Only remaining problem is their ability to hit my whole party with Daze, but I guess that's just what I'll keep Bahamut on standby for.