Dreykeo, I do not play either 'Nids or DkoK, and also agree with a general view that this might not be the best match up. However you also seem to be missing out on a number of key parts of the E:A rules and general strategy and tactics which would improve your chances.
Terrain is key for the Nids - do you have enough pieces that are a minimum of 10cm x 10cm (there should be 12 in the tournament game). Powerful as they are, Shadowswords (and most other formation so) can only shoot what they can see, so stay behind terrain or better, in it and more than 10cm from the front edge. Even when formations can shoot, usually they can only shoot units at the front of the formation - positioning of units is key, so make sure your 'fodder' surrounds more valuable units. Your greatest enemy is actually barrage templates, but clustering in terrain will mitigate their effect, especially ruins, as you can use the terrain cover value to save from hits. If all else fails, try to set up many threats, so that at least one will get through . . .
Formation composition is also key. Having tunnellers that can 'drop in unannounced', 'cannon fodder' formations to soak up enemy fire, Harridan strike formations for objective grabbing, duplicates of important units and redundancy where necessary all help you to achieve your strategic aims. Nids are one of the few armies where activation count is less important than unit numbers. If you have a WE formation (Dominatrix) add other WE to soak up hits, or even consider several such formations. Also place cheaper formations in front of your key ones to ensure you can spawn to your best advantage.
Finally you need a strategy and should place your Objective markers to match it. You should have several possible deployment plans in mind depending on the opponents army, the setup up choice and where Objectives are placed, and you should have good idea of the intended role for each formation, preferably with a secondary role to add redundancy into your plan.
Note, none of the above is foolproof (especially with my dice
) but following these general guidelines will help. And if all else fails, try counting the ones thrown, so you have an excuse for losing . . .