What are Synthesis Effects?
Synthesis effects are hidden passive effects that can be triggered on your characters. Some of them are very powerful and help a lot against difficult enemies.

How do Synthesis Effects work?
The game never tells you, but every single equipment piece and weapon in the game belongs to a Synthesis Group, there are 29 different groups in total. Combining on the same character several items belonging to the same Synthesis Group, triggers the activation of a Synthesis Effect.

Where can I find a list to know the effects and groups?
On the official wiki. Click here to open a link to the complete list.[strategywiki.org]

You just have to check what group each item belongs to, and what Synthesis Effect is derived from that group, and then equip the desired combination on a character.

Synthesis Effects stacking
The more items belonging to the same Synthesis Group you have equipped on the same character, the more powerful their derived effect becomes. Example, with Physical Wall;
1 item: No Bonus
2 items (of the same group): Physical Wall 5
3 items (of the same group): Physical Wall 10
4 items (of the same group): Physical Wall 20
5 items (of the same group): Physical Wall 30
- Thanks to Xzait for this information.

About Upgrade Materials
Basically, all the materials you use to upgrade gear (accessories, weapons) are of two big categories: Organic Materials, the one with the "fang" symbol, and Artificial Materials, the one with the cog symbol. This is a lot more important than you may think.

Ok, fine, but how do Efficiency & Multipliers really work?
When you use an Organic Material to upgrade a weapon, generally it will give very low XP, but here is the big deal: Organic Materials make the HIDDEN EXP Multiplier go up. After using organic materials for a hidden total of 501 points or more (use Sturdy Bones) the multiplier will become x3, which is the highest possible. That means the next ARTIFICIAL upgrade material batch you use will be multiplied x3 in experience!

So the procedure for the best efficiency is: first use 36x the cheapest Organic Materials on an item, get that sweet x3 multiplier, then jam in the most powerful Artifical Materials you have, to maximize the x3 bonus utilization. I personally recommend using Turbojets early on, then Perfect Conductors, and later on Ultracompact Reactors, these are the best Artificial Materials for the cost and how much XP they give.

ORGANIC MATERIAL STATS
Name: +(UpgradePointsPerUnit) - (NeededAmountFor x3 Multiplier):
Scaled Wing: +12 - Need 42
Thickened Hide: +11 - Need 46
Bestial Claw: +10 - Need 51
Barbed Tail: +14 - Need 36
Sturdy Bone: +14 - Need 36 <- your best choice
Vibrant Ooze: +14 - Need 36
Iron Shell: +13 - Need 39
Wicked Fang: +13 - Need 39
Enigmatic Fluid: +12 - Need 42
Fragrant Oil: +12 - Need 42

x3 Multiplier Amount changed from 45, which was wrong, to 36. Thanks to bowlonoodle.

Added a note about certain 80 gil tier materials giving slightly more XP in upgrading. Thanks to xxroid for the info.

Added organic material statistic list and corrected the value needed to achieve a x3 multiplier. Thanks to Xzait for the info.

About Shrouds and drop rates
So you may have noticed Shrouds are among the rarest and later on, when you can buy them, most expensive items around. Especially Deceptisol, useful for triggering pre-emptive strikes that can give you a decisive advantage in battle.

Well, shrouds may be very rare to drop apparently but there is a series of hidden mechanics and drop rates to help you get a LOT more and save money as well by not buying them.

What are the hidden mechanics about Shrouds?
The first thing you want to know is that the Drop Rate of Shrouds is higher when your combat rating is LOWER. That's right! If you get 0 Stars in a fight, that will give you a LOT more (8x to be exact) chances of getting a shroud.

The second thing is that some areas of the game have MUCH higher chance of dropping shrouds than others. Many of these areas can never be visited again as well. Here is a list of the areas and relative drop rates:

Pulse Vestige - 12% <- Best farming (12% x8 with 0 Stars = 96% chance) (No Aegisol here)
Lake Bresha - 8%
Vile Peaks - 6% <- Aegisol only starts dropping from here on. (Thanks to xxroid)
Sunleth Waterscape - 3%
Palumpolum - 2.5%
Nautilus - 1.25%
Palamecia - 1.25%
Gapra Whitewood - 1%
Fifth Ark - 1%
^ All of these above are ONE WAY TRIPS, you can't go back there once you leave.
Gran Pulse - 0.3%
Eden - 0.38%
Orphan's Cradle - 0.13%.

Fighting a Behemoth in the Fifth Ark (who drops Aegisol as a Rare Drop).
Delay the fight to either a 1 star or Zero star match rating and your chances of getting a shroud go up exponentially (5 aegisols in 10 fights) (Suggested by: NoName)

Every rate +5% using Survivalist Catalog. You will find this item pretty late though. That +5% with the 8x of 0 stars is a real blessing and if you are already in late game it is your best chance for the grind. Multiple catalogs DO NOT STACK. Always +5% MAX!

So by the list is clear you should take your time and stock up in the Vestige as those shrouds, particularly Deceptisol, will be mighty useful later expecially for tough A grade mission bosses. Trust me, it's worth the pain to grind this early.

What is Death Magic?
Death is a powerful but highly luck based spell you will get in late-game, as far as I know only Saboteur Vanille can use it. This spell has a base 1% chance to instantly kill any enemy, no matter how strong, even bosses. Some enemies are immune to it, so before wasting your time, check with Libra if they have immunity.
You WILL need this spell late in the game for some incomprehensibly powerful and nasty optional bosses. So read well.

What about the success chances?
1% is a very low chance. But thanks to hidden mechanics can be increased significantly.

Here is the trick: every negative status effect an enemy has (Deshell, Deprotect, Imperil and so on) increases the Success Chance of Death by 1%. Since the maximum amount of negative effects on a single enemy is 8, the chance can be theoretically ramped up to 9%. It is very unlikely any enemy worth using Death on may have all 8 negatives together, but 5-6 is totally possible even on high level enemies.

Death is very useful for getting the Growth Egg, an accessory that doubles CP gains in exchange for one slot on the active team's accessory slots! (Mission 55).

Thanks to xxroid for additional information about negative status effects.

Whenever you are in a battle, you can switch paradigms and have an immediate full ATB charge if done correctly.

To do it you need to expend 2 full bars of ATB in whatever paradigm you're currently in. After you spend two, the moment you cast the final spell, instantly switch to a new paradigm and you'll have a full charge to use again immediately.

This can be especially helpful later on when fighting adamantoise and long gui when running multiple Cerberus paradigms to keep your DPS as high as possible.
- Suggested by: jiglepuf

One important thing to note, is that if timed properly you can activate it after 2 full bars including the bar you forced to be full previously. Furthermore, you can also force your ally/allies to have full bars as well if you pay attention to their attack patterns as well
- Suggested by: Xzait

Another important thing is that when you start a fight, the very first time you swap your paradigm regardless of situation, you will have a full ATB Gauge.
- Suggested by: Xzait

Did you know, that Synergists actually have an order in which they cast their buffs? If you were wondering why your Synergists refuse to cast a certain buff over others, this order list will help you to understand why they cast it in a specific order.

The order usually goes in this order, making sure each character has it before moving to the next:

Haste

Buffs dependent on enemy notes in descending order of the list of notes:
"Delivers devastating physical attacks" - Protect / Protectra
"Executes powerful magic attacks" - Shell / Shellra
"Employs powerful (elemental) attacks" - Bar(element) [Well, except earth and aero... you might want earth/aero resistance here]
"Capable of inflicting Debrave" - Veil and Bravery / Bravera
"Capable of inflicting Defaith" - Veil and Faith / Faithra
"Capable of inflicting Deprotect" - Veil and Protect / Protectra
"Capable of inflicting Deshell" - Veil and Shell / Shellra
"Capable of inflicting Curse" - Veil and Vigilance
"Capable of inflicting Pain / Fog / Slow / Daze / Poison / Imperil / Death" - Veil ONLY
"Susceptible to Curse and the effects of Vigilance" - Vigilance
"Vulnerable to (elemental) damage" - En(element) [Well, except earth and aero again, so...]
"Vulnerable to physical damage" - Bravery / Bravera
"Vulnerable to magical damage" - Faith / Faithra

Then the Synergist casts any En- spell, depending on if the characters already has one or not.

Protect /Protectra, Shell/ Shellra, and Veil if not applied already

Finally, Bravery / Bravera, Faith / Faithra, and Vigilance if not applied already

Do note that Synergists, if they already see 8 buffs/debuffs on every character, and they cannot remove the debuffs, they will simply stop casting.

Because of this order, it's important to note that Bravery and Faith gets casted LAST in the order if things don't go well for you. Lets give an example: A enemy that's weak to fire but has no notes when you check with Libra will have the casts casted in this order:

Haste > Enfire > Protect > Shell > Veil > Vigilance > Bravery > Faith

Therefore, if you are noticing that you are not getting Bravery / Faith very quickly, it's important to either cast it yourself, or equip accessories that would give you it automatically, to save some time.

Remember the 5 part boss in Chapter 7, that can't seem to be hit with physical attacks, so you had to magic optimize Lightning, Fang, and Hope? Well, Lighting, wielding a gunblade, actually benefits from going Strength orientation instead because she CAN hit all the parts with the Attack command (which must be manually inputted! Auto battle will give you a line of Ruins). If you don't believe me, try it out and see how much more damage Lightning can do.

All my knowledge on the topic is already in the guide. And is very possible not all hidden mechanics are there yet!

If you know more of them, post in the comments and I will add them. With credits of course!