The Monk Temple

[Riot55]

I just beat Twintania a few nights ago, so here's what I can say about TP conservation in that fight and what I do:

-I only use Fracture when I have either Blood for Blood and/or Internal Release on, never without buffs. If at all possible try to time you buffs to fit in all your DoTs so they can be on the cycle (same thing with off GCD skills like Howling Fist and Steal Peak, which I save for burst during buff times, or whenever they pop if I know they'll be ready before buffs are available again)
-Perfect Balance immediately on the dragon adds at the beginning to get going and just Shoulder Tackle over to Twin after they're dead. You'll have PB ready again by the time conflags start just in case you get targeted. Additionally, it'll likely be ready about the time where you have to burst down the big snake before her big limit break. If you're struggling with killing the big snake (Asclepias?) before her limit break, pop a Mega-Potion of STR when all the mini snakes are dead and she has the debuff. The additional 60-some strength does wonders, especially if everyone in your group is popping potions. Your potion will also then be ready about the time you get down to the last 15% of her life when you need to burn her fast. We did an attempt and got her down to 1% and she hit her enrage timer and killed us... needless to say we were pretty upset, and potions could have helped.
-You will find yourself needing to use Invigorate after 2-3 rotations when you get to Twin after the dragons. Use it then and around the first conflag or so when the necklace breaks, have your Bard do TP song for just a little while, which will tide you over until divebombs start. Really just having it on for 30-45 seconds will give you what you need to last until you get a little break, and after that it shouldn't be much of an issue.
-Stay on the big snake the whole time during that phase. Let your mages kill the little ones so you can get as much damage in on the big guy. Kill the right little snake first, move back for divebombs, kill the second snake during or after divebombs quickly, run up with the big snake to intercept the other little ones coming across the map, let the BLM aoe Limit Break the other snakes, and help finish the little ones off if need be. MAKE SURE to try and avoid their death explosions, which puts a debuff on you. Remember to pop those potions!
-When Dreadknights start spawning, run away from where they pop so you don't get targeted and jailed close, and ALWAYS Shoulder Tackle over to them. The lowered CD on this move was the difference maker in this fight. Shoulder Tackle + Steal Peak + PLD/WAR stun should make all of them easy work.

Uhh, there's probably other things but I'm forgetting them. Just always make sure you are mindful of using extra abilities off GCD properly and smartly, work on your timing with your buff schedule, don't rely on Fracture every time it drops off (same thing with Touch of Death sometimes, if I have to let it stay off for a few seconds because BFB or IR is about to get ready, leave it off), and just maximize your positioning and TP coordination with a Bard. No bard? Well, uh, good luck I guess! It's not that hard, just hope for a conflag I guess =) Or just take it a bit slower.

[Atreides]

-When Dreadknights start spawning, run away from where they pop so you don't get targeted and jailed close, and ALWAYS Shoulder Tackle over to them. The lowered CD on this move was the difference maker in this fight. Shoulder Tackle + Steal Peak + PLD/WAR stun should make all of them easy work.

That is actually not the smartest thing to do, your shoulder tackle stuns it for 2 seconds and trigger diminishing returns, doing that turns a possibly 9 second stun chain into 5-6, while it may be enough for some groups, others might struggle.