This guide will cover:
1) How to download Dangan Pirates (KT entag game) on iTunes app store even when you're living outside Japan. (I don't use android, so I can't help you for that platform.)
2) Some basic things to look out for in order to get the KAT-TUN cards.
This entry is intended for players who have a minimum understanding of Japanese. The whole game is in Japanese, it's going to be challenging if you can't understand the language at all. I try as much to be specific but I'm sorry my real life won't allow me to answer many questions after this entry. And many thanks to
starry_glitter for all the game tips(^-^)/
How to download Dangan Pirates (KT entag game) on iTunes app store even when you're living outside Japan
1) Follow the guide here.
[ETA 2013/4/7: I've just been alerted that under the Paying Option, "None" will not appear and you will be prompted with adding in your credit card information. To overcome this, after you changed your iTunes Store to Japan store (before creating new ID), search for 弾丸パイレーツ! and click install. You will then be asked to create a new Apple ID. Proceed as per instructions above. Since 弾丸パイレーツ! is a free game, the "None" option will appear in Billing Option.]
2) If you're reading this, I believe you would have an existing iTunes account based on your country of stay. Hence, you'll need to enter another (new) email address to create the Apple ID.
3) Contrary to the guide above, you'll need to enter a Billing Address. I just entered a fake one :3 & English is okay.

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4) After you've finished, you can log into your new Japan account on your iPhone. Search for 弾丸パイレーツ! in iTunes Japanese store and you'll see the game above. Download to start your adventure~
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Basic things to look out for in order to get the KAT-TUN cards
1) Upon clicking into the game, you'll be asked to sign in to your entag!/mopita account. You may already have one created to watch KAT-TUNx [entag!] movies last year.

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2) If you encountered the above screen after logging in, you will need to reinstall the app. That happened to me the first time I downloaded the game orz
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3) If you got the above screen, you're on the correct track. And you'll get ☆Koki's card once you click on 約束の地へ旅立つ!
~Koki's Card~
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(it seems that my iPhone can't view the entire card in one screen >.<)
For ☆Ueda's card, you'll need to complete at least 2 quests (章).
For ☆Junno's card, you'll need to level up to Level 10.
For ☆Nakamaru's card, you'll need to join a guild (ギルド).
For ☆Kame's card, you'll need to clear 4 quests (章).
For ☆Group card, you'll need to level up to Level 15.
4) It seems that we can only get 1 KAT-TUN card each day. However, it wouldn't cost you any energy points (体力) if you try to level up (until Level 30) & clear the quests within 24 hours of starting the game.
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5) The above is My Page (マイページ) where most of the game options are.
6) To join a guild, click on the white words that read ギルドに入って振分けゲット! (above Koki's card in screencap above).
7) To do quests, click on the blue button that read クエスト (below Koki's card in screencap above).

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7b) You will see the above page after you click on クエスト. To proceed, just click on このクエストを進める!
Above Koki's card, you will see that I'm already on my 4th quest (第4章), which means that upon completion, I'm eligible to get Kame's card.
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7c) You're on a quest now~ Just keep on clicking the blue button that reads まだまだ進む! to complete quests so as to level up.
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7d) When you level up, the screen will tell you in English "Level Up" so don't worry about missing it. You will see that I've leveled up to Level (レベル) 12 now.
And I think that should be all to get the KAT-TUN cards. Have fun!