9 life is a high mountain to climb in this case, and even if you put the Eternal Thirst on your Accursed Spirit, you wouldn’t be able to make it big enough to defeat Ardy by itself. You’ll need another source of damage, and for that, you’ll have to kill your Scuttling Doom Engine.
- Before Ardy’s turn ends, tap a swamp to add
to your mana pool. - Spend and pay 1 life to activate Cruel Sadist and put a +1/+1 counter on it. You are now at 2 life.
- Allow Ardy’s turn to end. Your next turn begins, and you untap all permanents you control (except for the Scuttling Doom Engine).
- Draw the Forge Devil during your draw step.
- Tap five swamps to add to your mana pool (one used as generic mana). Tap three mountains to add
to your mana pool (two used as generic mana). Tap and sacrifice the Generator Servant to add 
to your mana pool. - Spend
to cast Eternal Thirst on the Cruel Sadist. - Spend to cast the Forge Devil. When it enters the battlefield, choose for it to deal 1 damage to the Frost Lynx. The Forge Devil also deals 1 damage to you. You are now at 1 life.
- Spend to cast Festergloom and give all nonblack creatures -1/-1 until end of turn. Ardy’s Bronze Sable becomes 1/0 and dies. The Frost Lynx becomes a 1/1 with 1 damage on it, and dies.
- Put two +1/+1 counters on Cruel Sadist due to Eternal Thirst. The Cruel Sadist now has three +1/+1 counters on it.
- Declare the start of your combat phase, assigning your Accursed Spirit to attack. Ardy now has no creatures that can block it, so the Accursed Spirit deals 3 damage to him. Ardy is now at 6 life.
- Spend and activate Cruel Sadist, removing three +1/+1 counters to deal 3 damage to your Scuttling Doom Engine. You gain 3 life due to the lifelink granted by Eternal Thirst. You are now at 4 life.
- Spend to cast Ulcerate on your Scuttling Doom Engine. You lose 3 life, and are now at 1 life. The Scuttling Doom Engine becomes a 3/3 with 3 damage on it, and dies.
- Scuttling Doom Engine’s ability triggers. Choose for it to deal 6 damage to Ardy, defeating him.