First, choose the Christmas map and select easy mode.
Note: Activate "Display score" in the "Scores" menu to keep better track of your achievements.



Then, just fly around, collecting snowflakes, flowers (colored balls), killing ennemies and collecting bonuses.
After approximatively 12 minutes, ennemies (and allies) will start to spawn more frequently.



After playing a bit longer (20 minutes tops), there will be hundreds of them.
Shoot and then quickly switch to an other ennemy to kill them faster. Your allies (the flying transparent manta rays) will help you. You should get all the killing/collecting achievements in no time.
Warning: this will cause a lot of lag; So you will need a PC that's not made of wood.
For reference, I did it with an old intel i5 3570k 3.4Ghz (220$ cpu from 2012) and an nvidia GTX 1080.
Also, you can try lowering the resolution in the settings if it lags too much. There are other settings too but I haven't explored them.



The remaining achievements are sunburn and friend of flowers, and here's how to get them:



The Sun is that big red ball in the Christmas arena linked earlier. For it to appear, you'll need to use animator 3 or 4, as stated by sfnhltb. Use it to reflect your bullets to kill an ennemy.



For I like flowers you have to fly through 10 flowers in 5 minutes. Flowers are those pretty spheres of various colors and sizes. They heal you when you pass through them.
You can activate "Display score" in the "Scores" menu. Now you can see how many flowers you've already flown through on the top left corner of your screen.