Achilles Accelerator

Instant - Destroy this: Gain 1 action point. Activate this only if you've boosted this turn.

Arcane Barrier 1

Rulings

From the Arcane Rising release notes

An action point allows you to play action cards and action activated abilities as they require an action point to play. (Not to be confused with resource points which are used to pay costs)
The boost does not need to be successful. You can use Achilles Accelerator after banishing a non-Mechanologist card from a boost cost.
When this card is destroyed, it is sent to your graveyard.

Keyword notes

Arcane Barrier - is one of the most common ways to prevent arcane damage. If you would be dealt arcane damage you may pay X{r} instead to prevent X arcane damage that source will deal.

You can have multiple instances of arcane barrier.
You can only prevent one arcane damage per arcane barrier per source.
You can prevent arcane damage you do to yourself.
Players cannot respond to the prevention.
To fully prevent a card dealing 3 arcane damage, you would require 3 arcane barrier and 3 resources to prevent it. To fully prevent 3 Runechant tokens (3 instances of 1 damage). You would require 1 arcane barrier and 3 resources to prevent it.
Preventing arcane damage does not destroy the equipment with arcane barrier (unless otherwise specified).
Arcane barrier is a replacement effect. It does not use the chain. Players cannot respond to the prevention.
Each source of arcane barrier can replace damage 1 time per source. To fully prevent a card dealing 3 arcane damage, you would require arcane barrier 3 and 3 resources to prevent it. To fully prevent 3 Runechant tokens (3 instances of 1 damage). You would require arcane barrier 1 and 3 resources to prevent it.
If a card has Arcane Barrier 2, you must pay the full two resources even if it only prevents one damage. You cannot choose to pay one resource to prevent one damage.
You can have multiple instances of arcane barrier, for example Nullrune Hood, Nullrune Cloak, and Nullrune Gloves.
Arcane barrier can be used every time you would be dealt arcane damage. It’s not limited to once per turn.
Each instance of arcane barrier you control can be used 1 time only, each time a source would deal arcane damage to you. For example if a source would deal 5 arcane damage to you, and you control two cards with arcane barrier 1, you will in total be able to prevent 2 arcane damage this source would deal to you.
To fully prevent a card dealing 3 arcane damage, you would require 3 arcane barrier and 3 resources to prevent it. To fully prevent the arcane damage from 3 Runechant tokens (3 instances of 1 damage), you would require 1 arcane barrier and 3 resources to prevent it.
A equipment with arcane barrier does not move to the chain when arcane barrier is used.
You can prevent arcane damage you would deal to yourself.
Players cannot respond to the prevention. Arcane barrier is a replacement effect, not an activated or triggered ability.
To fully prevent a card dealing 3 arcane damage, you would require 3 arcane barrier and 3 resources to prevent it. To fully prevent 3 runechant tokens (3 instances of 1 damage from difference sources). You would require 1 arcane barrier and 3 resources to prevent it.