Have you noticed that there are times of the year when you depend more on one lens rather than another?
I've noticed that as Autumn is approaching I'm starting to use my macro lens a lot more often. In addition it's great fun trying to photograph flying insects ...especially in mid air.
As a result I use High speed continuous shooting techniques to freeze those moments in time.
My High Speed Continuous Shooting Technique ...
I always use the high speed continuous shooting mode ...especially when photographing ladybirds.
My first handheld shot is never as sharp as the 2nd or 3rd shot. In continuous mode the shutter is pressed and held down. Consequently the 2nd shot onwards shouldn't show the shake from the mirror moving inside the camera.
I have an advantage as my Canon 7d shoots up to 8 frames per second. In fact it can shoot in bursts of 130 jpegs or 25 RAW files. Though very rarely will I shoot as many files as that in one go!
Make sure you are using the fastest flashcard that your camera can handle.
Don't buy a really fast one just for the sake of it as you'll be throwing your money away. Check with your camera manual first.
I try to manually focus. I don't rely on my camera to focus for me as I can't guarantee that it will focus on what I want focused. Plus the Tamron Macro 90mm lens in my opinion is a bit of a roamer. It's slower than my Canon 50mm lens in automatically seeking and locking the focus point.
I try to shoot at f5.6 - it's tack sharp and it's the sweet spot on my 90mm lens. Furthermore I don't use a tripod. So I make sure that my shutter speed is high enough to capture the movement.
The alternative is to use the in-camera auto DSLR focus mode which will track your subject. In Canon it's referred to as El Servo mode.
Give Your Subject Room in the Frame
Sometimes I prefer to just use the 50mm or 28mm. There is more space in the frame for the insect to fly into or fly out of. Though I'll probably have to slightly crop the final image. The space is a lot tighter when I use the 90mm and there's more of a chance of me not getting all of the wings in the frame...but there is rarely a need to crop.
Keep both your eyes open so that you can see what else is flying nearby that might come into your frame.
You'll find that a professional who shoots any type of sport will do this and it's no different for nature photographers.