This deck has taken 2 forms as of late but both rely on playing a lot of artifact acceleration. This deck does not play much defense but plays a heavy offense to get ahead of you with card draw.
Playing counter magic or prison pieces is often not enough to stop this deck if it is performing well. Timing is a critical piece of the puzzle, you must always be aware of the board state and their hand. You can just lose to Vault/Key lock.
Null Rod and Stony Silence are very good against this deck but is by no means a lock. Damping Sphere has not proved to be a silver bullet to stop this deck either but time will tell. Hurkyl's Recall can be very disruptive to all builds of this deck if it is played in response to a Paradoxical Outcome.
If they get a Monastery Mentor or Blightsteel Colossus they you will need something to remove these. You would assume that their weakness is time since other decks can pressure them but that is not correct. Sometimes, they will just wait for you to act.
Question about this deck: how many cards should be on your sideboard for this deck? If you are a Shop deck then you will want Null Rod but that hurts you too. How do you play past that? If you are a Xerox deck Hurkyl's Recall is good against this and Shop but Hurkyl's Recall does not beat this deck. Playing counters spells can disrupt them but most Paradoxical players expect a good number of their spells to be countered.
When I played this deck against LandStill I would just keep pushing broken spells until I got there. My top decks were better than theirs.
Most strategies against this deck are to bring in 2 to 4 cards to stop them such as Mindbreak Trap and Null Rod. I am not sure that is enough to stop them if their deck is performing well.