There are so many descriptions of skillchains in Final Fantasy XI, and none of them really made sense to me for the longest time. Through the help of a skillchain discussion and two skillchain charts, I finally made sense of it all. This is an explanation of that understanding; hopefully others will benefit from it.
Skillchains are the result of doing weapon skills in a particular order, with precise timing. They unleash a significant amount of additional damage. [There appear to be rough calculations on how much, but I can’t find reliable numbers.] There are three levels of skillchains—the higher levels do more damage. Every skillchain has at least one elemental component—if a mage casts an elementally-appropriate spell at the same time that the skillchain occurs, you also get a magic burst for more additional damage.
The items in the graph are also color coded to indicate their elemental attributes: Transfixion is Light, Liquefaction is Fire, Impaction is Lightning, Detonation is Wind, Compression is Dark, Scission is Earth, Reverberation is Water, and Induration is Ice. The above example is Liquefaction, so you could magic burst with any Fire spell.
Finally, some weaponskills have multiple skillchain attributes. For each skill there’s an order of priority. An example is Spinning Axe, which has, in order, Liquefaction, Scission, and Impaction. If you have two weaponskills with multiple attributes, the first skillchain’s priorities are more important. Let’s chain Spinning Axe with Shadow of Death, which is Induration and Reverberation. The first priorities of each weaponskill are checked first, but there’s no Liquefaction -> Induration skillchain. So the game goes down the list of the second weaponskill, trying Liquefaction -> Reverberation. Nothing. Now it goes to Scission on Spinning Axe and starts over with Shadow of Death, checking Induration. There are no Scission -> Induration chains, so it next checks Scission -> Reverberation. That is valid, so the two will form a Reverberation skillchain.
Skillchains themselves can be chained. You can go Scission -> Reverberation -> Induration, which will make a Reverberation skillchain followed by an Induration skillchain. When you do this, the damage multipliers are higher; the Induration skillchain would do more damage than if it had been created separately.
That covers level 1 skillchains, and is really most of the hard stuff. Now we go on to level 2.
As with the level 1s, you can hook together multiple level 2 skillchains. You can do things like Liquefaction -> Impaction -> Gravitation, which will make a Fusion skillchain followed by a Gravitation skillchain.
The usual rules of chaining apply; you can make, for example, a light skillchain with the sequence Liquefaction -> Impaction -> Fragmentation, which will first make a Fusion skillchain followed by a Dark skillchain.
Insofar as anyone knows, there are no level 4 skillchains. Following the logic from lower levels, there would only be one level 4 skillchain, and it would have all elemental attributes. It would be made by putting together a Dark type and a Light type weaponskill (possibly in the other order). It would require weaponskills that had Dark and Light type attributes, which none seem to. In short, not only do they not exist, as far as anyone can tell, they cannot exist in the game as it currently is.
For your edification, here’s a full chart of the links to form the various skillchains:
I don’t know of any complete, up-to-date list in English of weapon skills and their skillchain attributes.