I just got the Level 20 achievement yesterday, and thought I'd share a few tips for those struggling. I'm by no means an expert, but I hope this helps at least someone.
Take your time - I cannot stress this enough. Plan every move and always remember to check the queue after every flower placement as the 4th flower in the queue could change your next flower placement.
Try to group similarly coloured flowers together. This may seem obvious, but keep an eye out on the colour the flower will transform into after it's popped. Sometimes it's worthwhile not completing a chain if you will end up boxing yourself in when a double flower transforms into a colour that has no adjacent coloured flowers.
Go round the edge of the board. String colours together round the outside of the board instead of from the edge to the middle and always try and leave room to complete a chain of at least 3. for example if you place a red flower so it blocks off a chain of 2 blues, then you've wasted 3 spaces on the board unless you know you can get rid of the red before a blue comes along.
Remember to place unfavourable flowers in blocks that will be filled in when you reach the next level.
It's difficult, but as the game progresses into the later levels, resist the urge to place colours together if there is no way you can complete the chain because of the boundaries of the grid. This is also why it's better to form chains around the outside of the grid as opposed from the edge to the centre - Two colours next to each other with nowhere to place a flower at either end won't help you at all!
From about level 14 onwards try and get into the mindset of just clearing the board and forget about points. Be as efficient as possible and always plan 2-3 moves in advance.
Keep trying, and good luck!