Perfect clear the specified stage
Building Cannons on the top row to take out the first wave of enemies
and then build a Arrow Tower on the tree closest to the base and upgrade it till you get the yellow flag.
Wave 4 and 5 you are going to need to buy the Laser Towers so make sure to save your gems. Build the tower at the the start of wave 5 and upgrade it till you get the red flag. Build two more Laser Towers and upgrade one to red flag and the other to yellow.
Build Fire Towers at around wave 11 or 12 and upgrade them to purple flag as quickly as possible. I suggest placing these near the entrance.
Once you've achieved this immediately go back to working on the Laser Towers get them to purple as soon as you can.
After getting them to purple save up and build as many Fire Towers as you can getting them to purple every time. Be sure to try and place more of these towers on the left side then the right.
Before you the boss arrives on wave 20 replace all the arrow towers with either cannons or fire towers and upgrade the replaced towers as much as possible.
4 Tree Rainbow
Perfect clear the specified stage
This is a really hard trophy if you don't know which towers to use simply use the towers as listed below each tower represents one of the trees.
WAVE 1 - Blank, Cannon, Cannon, Arrow
WAVE 2 - Arrow, Arrow, Arrow, Arrow
WAVE 3 - Cannon, Cannon, Cannon, Arrow
WAVE 4 - Air Gun, Air Gun, Cannon, Arrow
WAVE 5 - Cannon, Cannon, Cannon, Arrow
WAVE 6 - Arrow, Arrow, Arrow, Arrow
WAVE 7 - Cannon, Cannon, Cannon, Arrow
WAVE 8 (Buy Fire Tower) Air Gun, Air Gun, Air Gun, Arrow
WAVE 9 - Fire Tower (Upgrade to Yellow Flag), Fire Tower, Fire Tower, Arrow
WAVE 10 - Fire Tower, Fire Tower (Upgrade to Yellow Flag), Fire Tower, Arrow
WAVE 11 (Buy Mortar Tower) - Fire Tower, Fire Tower, Fire Tower, Mortar
WAVE 12 - Air Gun, Air Gun, Air Gun, Mortar (Upgrade as far as possible)
WAVE 13 - Mortar (Upgrade as far as possible), Mortar, Mortar, Mortar
WAVE 14 (Buy Laser Tower) - Mortar, Mortar, Mortar, Mortar
WAVE 15 - Mortar, Mortar, Mortar, Mortar
WAVE 16 - Mortar, Laser, Laser, Mortar
WAVE 17 - Mortar, Mortar, Mortar, Mortar
WAVE 18 - Mortar, Mortar, Mortar, Mortar
WAVE 19 - Mortar, Mortar, Mortar, Mortar
WAVE 20 - Mortar, Mortar, Mortar, Mortar
Clear the specified stage using only arrows and cannons
This is a pretty hard trophy to achieve due to the fact that only Arrows and Cannons can be used. It also helps a lot knowing you can use mines. Play it like any other level and use mines when needed. I recommend using at least one for 19 since the enemies are resistant to Arrows and Cannons.
Clear the specified stage by building every type of tower
Another pretty easy trophy simply save all your gems for unlocking towers instead of using them for quick upgrades. Just look at the enemies coming in the next wave and you will know what tower to unlock. Start off using Arrows and Cannons and be sure to place an Ice Tower because it will be needed so make sure it can reach the enemies.
Clear the specified stage without crossing the bridge
Build Arrow and Cannon Towers at the entrance of the bridge. Be sure to save your gems for Laser Towers and only build Anti-Air Guns when needed which you should only have a max of 3 if even that. Right when you unlock the Laser Tower build one in the group of trees by the bridge and 2 more up top by your base. This should be able to hold the next couple of waves that come through. When possible build 2 Fire Towers at the entrance of the bridge and upgrade to red flag immediately.
Clear the specified stage without a tower ever upgrading
This is a slightly hard trophy to get you just have to pay attention. Check all trees for gems and coins. Be sure to constantly be checking towers because every enemy they kill will give them XP. When you get enough gems buy interests and keep doing so until the end.
Clear the specified stage without using the fire tower
Really simple just don't use the Fire Tower and instead save your gems for mines and use them when necessary.
Clear the specified stage with 25 or more gems
This level is a little more complicated then the rest. Due to the fact that there are only 22 gems on the level and 1 hidden in the trees. So how do you get the last 2 gems you ask. Good question you can either upgrade 2 of your towers to purple and sell them which both will give you a gem or simply upgrade 1 tower to black and sell it which will give you 2 gems.
Clear the specified stage with a balance of 10,000 worth of coins or more
Start out building a few at the entrance and a few by your base, then simply upgrade the towers and only make new ones when needed. Sell towers you don't need and be sure to put all your gems towards buying interest.
Bomb The Boss
Clear the specified stage using only bombs to destroy the boss
Play like any other level and save all your gems. When it comes time for the boss sell every tower you have and buy mines and place them where he walks then detonate and repeat until he's dead.
Clear a stage without losing a single coin
Easy to do simply search all the trees for coins and pick up the coins the enemies drop. Recommended stage: Easy 3
Build 10 towers in less than 30 seconds upon entering a stage
Once again select the stage Easy 3 which starts you out with 1000 gold and build 10 Arrow Towers right away.
Clear an entire wave of enemies with only a bomb
Do this on the first non tutorial stage and when the wave of 2 golems come simply buy a mine and blow them up.
Destroy 15 enemies at once with the Mortar Tower
Hard one to explain so do as the video shows.
Credits to Danboly for the Video
Encore : Black Flag
Without selling any towers, clear the specified stage with all towers upgraded to black
Go to the right of your base and simply place 4 Cannons, 3 Arrow, and 2 Anti-Air Towers. Upgrade them all to red flag and then after building your first Anti-Air Tower make sure you have 7 gems to upgrade it to black flag right away. Once all the flying enemies are dead you will get a lot of coins and gems. Sadly you will lose 1 or 2 from your base but you will still receive the trophy.
Encore : Scrooge's Return
Clear the specified stage with a balance of 12,000 worth of coins or more
Do the same as you did to get the first Scrooge Trophy but for this one you will have to sell a few of your towers in the end to reach 12,000.
Encore : Wishing Well
Drop 100 coins into the water and clear the specified stage
Just build an arrow tower near the water and sell it, most of the coins go in and just repeat until you get the trophy.
Encore : Zero Carat
Clear the specified stage without using gems
Easy just play like a normal level just don't use any of your gems.
Encore : Lucky Find
Find an extra large stash of coins and gems
Really easy level again, play the Treeless Forest/4 Tree Rainbow until you find a gem and some coins in a tree. That's the stash. (You might have to play multiple times to find it)