https://www.youtube.com/watch?v=m68pc8ZVPG4
The feat happens around 1:40 in here. Later in the game you fight a bunch of these guys with a sword, so the reactions scale to just about everyone. These people are also capable of deflecting every gun in the game, of which the highest muzzle velocity is 884 m/s.
Now the distance travelled by the Tengu looks difficult to figure out on the surface as the animations don't match up to what is happening. However frame-by-frame analysis consistently shows the "bullet deflect" occuring around the middle of the swing, each of which is at least 180 degrees wide. Backing this up is that you can see them deflect bullets even when their arm is out to the side, which would logically require at least 90 degrees of movement.
However I would like to say that the way they hold the sword during the animation shows they don't extend it out much farther than their arm's reach. Because of that I will not be accounting for the blade's length as the entire radius is basically equal to the length of their arm.
http://i.imgur.com/UDuQpZ4.png
Raiden Height - 182 cm (shown as Snake's height in MGS2) or 222.91 px
Distance to Tengu - 223 px
222.91/223 = 0.999x
182*0.999 = 181.81 cm
Now the issue with getting the Tengu arm length is that there are 2 Tengu in that frame, so I'll need a different picture. The model for the Tengu is also about Raiden's height, so I'll be using 182 cm for them as well.
http://i.imgur.com/Aj2MM9b.jpg
Tengu Height - 182 cm or 293 px
Tengu Arm Length - 129.61 px
129.61/293 = 0.442x
182*0.442 = 80.44 cm
Circumference of a Circle = (2)(pi)(r) = (2)(pi)(80.44) = 505.42 cm
505.42/4 = 126.355 cm
So now it's just a ratio of distance moved compared to the bullet.
126.355/181.81 = 0.695x
884*0.695 = 614.38 m/s
Now just to be safe I'll high-end it and assume they move 180 degrees per swing before the bullet hits (even though this wouldn't make sense at all). That would double the distance and give us 1228.76 m/s.
I have been informed that the Tengu can block these bullets from any range. Therefore I will use the smallest distance possible, that of the gun barrel. The length of the M4 barrel is 0.368 m, so now we just do the ratio again.
1.26355/0.368 = 3.433x
3.433*884 = 3034.77 m/s
Results
Tengu Speed (Realistic) - Mach 1.81, Supersonic
Tengu Speed (Unrealistic High-End) - Mach 3.61, Supersonic+
Tengu Speed (Point Blank Block) - Mach 8.92, Hypersonic