CryptoSpades
Since Hatter has already done an excellent write up, I'll just briefly gloss over some really specific and nit-picky things that I think are worth mentioning. Many of these points are at least somewhat addressed in 0neye's ship building guide, which is definitely a critical resource.
- In general, ships of this size are generally inefficient. Due to how weapons in Cosmoteer work, it is difficult for ships of this size to readily use all of their available firepower, as most weapons are side mounted with somewhat limited range. This means that larger ships such as this one can struggle to focus fire on threats on any effective manner.
- Speaking of firepower, the vessel here seems a bit short on it, especially given it's size. With only 22 small lasers, 20 standard, and 4 large cannons, and a smattering of other weapons the ship feels like it lacks signifigant firepower, especially in relation to it's high cost (nearly 4.7 million credits).
- The ship is rather slow in speed. Self-explanatory, more thrust in all directions would be a nice improvement.
- There are probably way too many shields. I see that the intention appears to be covering all of the ship in shielding (which looks quite neat, I must say), but the amount of shields here is a bit extreme. This many shields will tax the crew and reactors, and in of themselves will contribute to much of the ship's expenses.
- From a competitive standpoint, sensor arrays and FTL drives are not particularly useful (or are outright useless), and only contribute to increase the cost of the vessel. I'm also not sure if sensor arrays stack (I don't believe they do), so having more than one is rather pointless.
Not a terrible ship for sure, and with some key improvements it could be a fearsome warship. Best of luck!
P.S. - This is not relevant to the design itself, but I am curious as to how you label your ship types. I see you call this vessel a "Super Destroyer" or an "Exotic Cruiser". You also state such a ship is designed to engage battleships. It's not of any importance to it's overall design merits, but I'm just curious as to where these terms and roles came from, as I've never heard of any naval force utilizing ships classed as "Exotic cruisers", and destroyers are never really designed to engage battleships. If it were me, I might label a ship such as this a cruiser variant, or a battlecruiser.
EDIT: Noticed that the ship lacks the lateral thrust to be able to move properly during combat, meaning it will simply turn to fire its weapons and then be forced to rotate back to a forward angle to move into position should the enemy move out of range. This is a major flaw that should be addressed.