Now when you have left your first arena and you are on a burning fire to reach Arena 12, you have a complete confidence (rather overconfidence) to unlock new cards faster. In this arena, we get to find some cards which are really tricky to use and needs practice. It is absolutely okay if you lose many battles and stay there for long. And do not tag yourself nuby and keep the confidence to move ahead to the Barbarian Bowl.
This arena unlocks cards like Minions (earlier) and Skeletons which will seem useless to you at the beginning (though Skeletons seem useless to me till now and I prefer Minion Horde to Minions). These cards need utmost talent and intelligence to be used. You get Bomb Tower (now available at Arena 10), the first defense only building, in this arena. You get troops like Balloon and Giant Skeleton which when get killed leave a bomb to damage enemy troops, buildings and/or tower.
A great trophy pushing deck for Arena 2 according to me is:
Giant: The tank which will shelter the swarming troops (the only troop type you mainly have) and will also be an asset for defence as well as offence.
Goblin Hut: The producer of constant troops which will help in a huge troop swarm. Can prove a great defence against Minions and also other splash damage units and even enemy tanks. Since you have no Rockets to destroy them. Yet you have to face Fireballs.
Musketeer: The newbies in Clash Royale are prone to carry new cards received in their playing decks. But in this case, they are correct, since Balloon can act as a good combination with Baby Dragon and Witch and/or Valkyrie.
Skeleton Army: Great defence against Mini PEKKA, Prince and a distracted Witch. But the use of only one Minions card or Arrows or Valkyrie can erase them from the Arena.
Prince: A great offensive card with only one weakness, Skeleton Army! So pair him up with Baby Dragon and/or Valkyrie. A Witch will also do (According to me, let the elixir fill up to 10 and then let both the Witch and Prince out but first wait until your opponent lets out his card. Always let your opponent let his card out.)
Baby Dragon: Only aerial tank until Arena 4 (but getting Inferno Dragon or Lava Hound is not at all possible without spending bucks, gems or sheer luck). Can clear off an entire swarm.
Valkyrie: Great splash damager. When combined with Prince removes the fear of Skeleton Army.
Witch: Similar but can also damage aerial units. Since spawns skeletons so great against Giant Skeleton.
Arrows: Clears off swarm and can even damage heavily weakened towers. Can make you win by a crown at last moment!
You will learn to use Minions, Tombstone and Bomb Tower later. Giant Skeleton and Balloon can be used instead of Giant and Musketeer respectively. But epic cards are very rare at this stage.