The point of immortals is to not be killable. Trying to kill them is against the point and you're going to have a bad time trying.
This begs the question: Why do you want to kill an immortal?
If you want to slow it down:
- Sanctuary, Shard of Gratitude, Vampire Stiletto mitigates its damage potential.
- Sundial, Shard of Sacrifice prevents it from dealing damage to you.
The downside of immortals is that they actually have a terrible attack/cost ratio: 6 aether for 4 attack and 7 aether for 5 attack upped. For reference, weapons tend to have 5 power for 3 quanta, and Psion has 4 attack and shield bypass for 4 quanta.
Now, chucking Shard of Wisdom onto these guys makes this a lot better, but you're still looking at 8/9 attack for 9 and two cards, which puts it on the same scale as dragons/nymphs.
Dragons, Nymphs, and immortals are extremely slow. By the time you've even cast an immortal, a proper rush deck can have most of its power up and running, even unupped - Grabbow can have a graboid and arsenic turn 3 for 14+ damage a turn. An immorush probably has a turn one lava golem - 5+ damage by the first turn and increasing. By the time you have that single immortal out, monolife has a frog and adrenaline for 12 damage a turn. It's an entirely viable strategy to be faster than the immortal deck.