Hi! Welcome to the Forum!
I was waiting for someone more skilled in circuit designing to take a look at your post. As nobody showed up, I'll put my 5 cents.
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Your tilt sensors are not connected to any pin of the Attiny, how do you expect their value to be read?
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The current expected to drive your 3V 1W LED is around 300mA. There's no way you can provide this current with an Attiny's pin. So, you can't finish the circuit without a transistor. By the way, even the coin battery is a poor choice because it can't give you enough current to drive such a LED and the rest of the circuit.
Being this your first post, is highly recommended that you read How to get the best out of this Forum. I can imagine what you're trying to do, but I'll only be sure if you tell.