When swiping in any direction, the entire level moves. Try to match as many squares as possible with each swipe and maximize the empty spaces. The more empty spaces, the easier it becomes to match more.
Empty moves are those that result in no matches. Reduce these as much as possible because each move you make places an extra tile randomly on the level.
Balance your growth and do not have one huge number and many small ones. Try to have about two of the highest level numbers at all times ready to be matched, followed by increasingly smaller amounts also in pairs and ready to be matched. If you get a single number to very high values, the level might fill before you get a new one to match it with.
Focus on matching the small numbers (2s and 4s) that you get for awhile. Do not allow them to accumulate space on the level. While matching and mixing the small titles, you will be creating bigger matches.
Swipe the level right, left and down only to build a nice base of tiles at the bottom. Then make a few moves and get some chains after swiping up to get very high numbers. Then, use those three directions again and repeat the process. This reduce where new tiles will appear and makes them easier to use.
The key is to watch out for open spaces. As you slide number tiles in all given directions - up, down, left and right - they'll shift depending on the number of open spaces. If you see an opportunity to add bigger numbered cards - for instance, 64 into 64 - don't hesitate to do it. This frees up space on the board, with one less tile to worry about. When you can, be sure to add smaller numbered cards. Otherwise, you could run into a situation where a 2 or a 4 card easily becomes surrounded by higher ones - and you won't get a chance to add it to anything.
The higher numbered cards you end up with on the board, the better the score. The overall goal is to get to a 2048 card, but as you might guess, that's a massive task. Add as many cards as possible to get bigger numbered cards, like 256 and 1024. The higher the points, the better you'll fare overall through the game's online leaderboards.
Various Google Play Achievements
How to unlock
Bear Grillz (3,000 XP)
Survive for 600 seconds (4x4).
Corporal (1,500 XP)
Create 256 tile in All modes (4x4).
Expert (10,000 XP)
Create 4096 tile (4x4).
General (5,000 XP)
Create 2048 tile in All modes (4x4).
Major (2,500 XP)
Create 1024 tile in All modes (4x4).
Newbie (1,000 XP)
Earn 1000 points in any mode (4x4).
Online King (2,000 XP)
Play 10 online matches in any mode.
Practicant (500 XP)
Get 512 Tile in Practice Mode (4x4).
Row of Eight (2,000 XP)
Collect in any vertical or horizontal row five tiles with 8 in 5x5 Classic Mode.
Row of Four (1,000 XP)
Collect in any vertical or horizontal row five tiles with 4 in 5x5 Classic Mode.
Row of Two (3,000 XP)
Collect in any vertical or horizontal row five tiles with 2 in 5x5 Classic Mode.