Nikon D5100 not sync with external flash?

I have a Nikon D5100 with a AF Micro Nikkor 60 mm lens. I'm using an F stop of 36, and Achiever 260 AF flash. Any speed above 1/250 the flash is too slow and only about halve of the screen catches the flash. Is there a way I can change the settings to sync the camera and the flash or a flash that I can buy that is compatible with this camera?

You'e asking the camera to sync beyond the shutter speed that it's built for. The D5100 is designed to sync at speeds up to 1/200, and no faster.

And if you're not using a Nikon SB flash with your camera, you're not fully embracing the great technology and capabilities of the Nikon Advanced Lighting System. A Nikon SB flash, unlike the Achiever, will set the shutter speed, f/stop, and even automatically zoom in the flash head to match the focal length if you're using a zoom lens.

Your camera has a focal plane shutter. ANY DSLR has a maximum synch speed - it's in your manual.

No flashgun in the world will do what you ask, and there's nothing wrong with either flash or camera - just learn to use them properly.

I guess you have this flashgun because it's either been hanging around for years or was dirt cheap. Old flashguns of this type are not going to manage any sort of High Speed Sync (HSS) so as George has already mentioned you'll be limited to maximum shutter speeds as low as 1/125 to 1/250 of a second.

If you want to use any sort of high speed sync then you have to look at the specs of of the individual fashguns. I'm no expert, but I would guess you are going to limited to the upper end of Nikon's own speedlight range, or certain flashguns from Metz and Sigma.

*For Andrew, I shoot with a Sony and it will flawlessly machine-gun at 12fps at 1/8000th sec with the external flash (with the flash set to 1/8 max or less).So this what's being asked is possible with modern equipment.

A Nikon brand flash can interact with the camera's electronics to tell the camera it is there. The camera should then limit itself to 1/200th sec. However, a generic, manual only flash may fail to do that.
Using your highest f number to maximize depth of field seems to make sense, but in reality your image quality at that setting won't be great due to diffraction. Sharpness will deteriorate steeply after about f16.
Look at the MTF resolution section on this page:
http://www.photozone.de/...28?start=1

If you mount your camera on a focusing rail and mount the rail on a tripod, you can avoid all of this needing a shutter speed faster than 1/200th second, you cameras highest flash sync shutter speed.

If your flash is supplying all of the light, then it does NOT matter that the shutter speed is slower than you wish or not. The flash duration of most flash units at full power exceed 1/1000th second. As you reduce the flash output, the duration of the flash becomes shorter. Some flash units at 1/16th power have a flash duration of 1/10, 000th second.

You are going to have to experiment until you get the right flash power setting to provide good exposure at f/32

The source I found shows that your flash has a Guide Number of 86/ISO 100

The more advanced Nikon Cameras (D90; D7000 and above) have a feature called Auto FP high-speed sync, which allows you to use shutter speeds up to 1/4000th of a second when using certain Nikon Speedlights.

Unfortunately your D5100, being an entry level camera does not have this feature.

Something to remember the next time someone states that the D5100 is better than either D90 or D7000.