With regard to Shadows, they don't seem particularly keen on defense.
They don't appear to rely on heavy armour or impressive fields. Concentrated fire from the weapons of the younger species can destroy their ships. When harmed in batttle beyond recovery, Shadow vessels self-destruct instead of floating around as wreckage.
Their home planet exhibited similar behaviour. It wasn't guarded by an impressive fleet, only the Eye - which could be expected to fail against better protected minds, like those of Vorlons or other First Ones. The reaction of Z'ha'dum (if it was their home at all, not merely a meetingplace) to an imminent threat of getting compromised, was to explode.
Shadow strategic weapons don't rely on armor either. Any component of their planetkiller alone, was easy to destroy. The entire structure however, was a loose, very spacious and allegedly self-organizing cluster of weapons and particulate matter, into which sensors could not see, and into which an opponent might fire a silly amount of weapons (including high-power bombs) without covering more than a fraction of the structure's volume with effective enough destructive power.
What they do rely on, is stealth, namely ability to appear next to their target, and deliver a strike under most common defenses. When destroying a Narn base by surprise, Shadow vessels appeared into normal space practically next to Narn ships, with their weapons already trained on targets. The only further action which was required of them, was to fire.
Their strategic weapons also rely on ability to pass through most obstacles. When a Shadow planetkiller fired its missiles at a planet, they appeared to have little difficulty passing through the planet's crust, and exploding inside. This would suggest that shields would be of very little use, against a weapon which a Shadow built to reach well-protected targets.
A serious consideration to keep in mind when fighting Shadows, would be their ability to build artificial life, including species of nanomachines, including such which compute in decentralized manner, and direct their own evolution to better fulfill their goal (whether it be destruction or doing something else).
However, Shadows were not seen using such tools / weapons personally. Only after their departure did their assistants and proxies, the Drakh, attempt to use such an agent against Earth. It was however a near-failure, most likely due to serious inability on part of the Drakh to instruct the nanomachines on what they should accomplish.
Whether a Shadow desiring to do this, could build a disease to infect the Borg, and if yes, whether it would be the equivalent of a deadly plague or the common cold, naturally remains uncertain. It would likely be capable of infecting both biological creatures and machines.
It might also be capable of infecting planets and building infrastructure to turn a planet into a fleet, but Shadows were never seen doing that (or building ships on planets). Instead they seemed to prefer smaller objects, traveling without a star, optionally in hyperspace. I suspect they would be more than capable of starting to consume planets, but considered planets too vulnerable and didn't prefer that.
As for Shadows personally, there is doubt on whether they can really de-materialize or not, and whether by turning invisible, they end up in hyperspace or elsewhere. However, basing on the depiction of a pair of fighting Vorlons passing through station walls without leaving a hole, it can be suspected that a Shadow might easily walk through matter as well. Potentially with casual ease.
As such, their ability to cleverly extract information from, implant information into, and thus sabotage or re-purpose a crucial system or person, ought be considered. Few creatures may have reason to be really certain in the integrity of themselves and their systems, while facing an opponent who is that difficult to notice, and wields that capable tools.
Yes, fellow First Ones likely aren't vulnerable to their tricks, their own complexity and physical properties resembling those of Shadows. But a less prepared creature ought likely be careful with them - they seem to rarely give any information without wishing to, but might easily take or modify information not intended for them.
