This deck fights for the early board, has some flexibility and draw to help it get to the end game, where it has near infinite N'Zoth, the Corruptors.
In the mulligan, you almost always want to favor card draw via Cavern Shinyfinder, Dirty Tricks, and Greyheart Sage. If you anticipate a quicker matchup, then by all means keep a 1 drop. If you have a Cavern Shinyfinder, then keeping Infiltrator Lilian can be good in all matchups.
You should always mulligan away Necrium Blade except maybe if you also have Infiltrator Lilian. The reason is because Cavern Shinyfinder only draws weapons. For this reason, you should always play him if you have the mana and still have weapons in your deck.
Zilliax and Khartut Defender help you survive into the late game. Assuming you were prioritizing card draw when possible, you should have N'Zoth, the Corruptor, Shadowstep, and Togwaggle's Scheme in the late game, allowing you to win under almost any circumstances.
Here is my intro and highlight games: