The combo relies on replicating the Southsea Squidface deathrattle for as many times as possible. Happily there's an efficient way to do it, featuring Unearthed Raptor as the deathrattle multiplier and a combination of Test Subject and Play Dead for an amazing amount of deathrattle triggers!
Having the right cards in hand, the combo is not hard at all to pull off, so the tough thing is to get Test Subject and Play Dead to your hand as a Rogue character. So in the following lines I'm gonna basically describe how I exactly got those cards in a strategy that's prevented from pure RNG as much as possible.
First off, you probably realised I'm playing both sides. I chose hunter on the other side so that I could use Swashburglar (in combination with Brann) an indefinite amount of times until I get Play Dead in hand. Regarding the Test Subject, I was kind of lucky to get it from a single Jar Dealer. But in case I would have failed the 1 in 141 chance, I would've needed the opponent to play Zul'drak Ritualist an indefinite amount of times until Test Subject get summoned on my side. Playing a Brann and a Zul'drak would result in 6 1-cost minions being summoned, so a couple more Zul'draks shall make it.
And lastly, the game was supposed to last for long. Rogues have an easy time surviving past fatigue turns with heavy shuffling tools, Lab Recruiter being among the better ones. Thus after getting to the Shadowcaster factory and drawing all the combo pieces, it's time for heavy amounts of shuffling.
But wait, how did the hunter survive the fatigue? For that, it needed some serious shuffling too. A weird workaround I figured out is, after rogue plays Lab Recruiter, hunter copies it with Faceless Manipulator. Then he plays Pack Tactics so it could possibly obtain one more. The rogue then hits the Lab Recruiter for 1 damage, thus the other 3/3 one is summoned, and then the rogue saps one of them, leaving hunter with the easy job of repeatedly shuffling the Lab Recruiter. (you can also try it with Zola the Gorgon, Bankful Banker, Youthful Brewster or even another Manipulator).
~ Some math and much fantasy: How much attack can we put on a single dagger?
The Raptors can retain a capped number of 16 deathrattles. All of them inherit the Squidface deathrattle "give your weapon +2 attack". So the maximum attack one could get from a Raptor is +32 attack, but Baron Rivendare doubles it, so it caps at a nice +64 attack.
Test Subject and Play Dead work as follows: once Test Subject is summoned, playing a Play Dead spell on him will immediatly return one Play Dead spells to your hand. Playing a Play Dead spell on it once again will return 4 Play Dead spells to your hand. Thus in the generic situation, after playing the N-th Play Dead spell on the Test Subject, it will immediatly return 2^N Play Dead spells to your hand, amount which may be truncated by the number of your free hand slots. So it comes out that after the third Play Dead spell you cast on it, it will just fill up your hand with Play Dead spells.
How many Play Dead spells can one apply to a fully charged Raptor? Probably 6, 7, 8 or 9 at most, depends on the free hand slots. Thus, suppose you repeatedly cast Play Dead spells 10 turns in a row. You're about to trigger Raptor's (+64 attack) deathrattle about 70 to 80 times, that means your dagger's gonna get around +4500 attack.
Suppose you then have Tess Greymane that could reply ALL your Play Dead spells once you play it. Then suppose you can infinitely shadowcast Tess, so that you could replay it with 1 mana. Suppose that you have 3 fully charged Raptors, one Baron Rivendare and the other 3 slots are there for the Tess and shadowcasting shenanigans. This way you can play around 1.5 (1 or 2, depends on the turn parity) Tess'es per turn. But how much attack can one Tess affect your weapon with? If you casted 100 Play Dead spells before, it is exactly +6400 attack. Playing 1.5 Tess'es per turn allows About +9600 attack on turn per average. Further, suppose you can repeat it for 20 turns (the game limit is 45 turns per each character). The result is a nice +192 000 attack on the original dagger. Finally, with perfect RNG and balanced turns, I guess the maximum amount of attack one could get is around 200 000.
Sadly, I could not achieve the dream, since I don't have Tess Greymane in my collection.
Have fun watching, and I challenge you to beat this.
:)