okay. here's what you do:
1: go to dosbox.sourceforge.net and download the latest version of dosbox (0.63)
2:run dosbox, and open up setup for tyrian. make sure that you have sound set up as follows:
music: fm sound
sound: soundblaster: dma 1
3:tyrian. press ctrl+f12 until it speeds up to normal speed for the game. note the cpu cycles emulated (in the upper right hand corner, it says cycles:x where x is the number you want). exit the game.
4:open dosbox.conf with notepad.
5:
there is a section that looks like this:
[cpu]
# core -- CPU Core used in emulation: simple,normal,full,dynamic.
# cycles -- Amount of instructions dosbox tries to emulate each millisecond.
# Setting this higher than your machine can handle is bad!
# cycleup -- Amount of cycles to increase/decrease with keycombo.
# cycledown Setting it lower than 100 will be a percentage.

core=normal
cycles=3000
cycleup=500
cycledown=20

cycles is set to 3000. change it to the cycles number you noted (6000 for me).
save the file.

you can make any other changes you want in the file, but this is all that's needed to speed up the game.

now there is also a small problem with delayed sound effects. just change the following in dosbox.conf to 44100:
rate, under [mixer]
oplrate, under [sblaster]
pcrate and tandyrate, under [speaker]

let me know if this helps.

Supposedly the latest CVS runs Tyrian 2k better than 0.63. Haven't tried it myself tho but since 0.63 came out waaaaaaaaaaaayyy back in NOV 2004 and there's been alot of changes since then, it's highly likely that it's faster with the latest CVS.

Speaking of shooters, do you have any idea when a shooter called Baryon will be more stable because at the moment with DOSBox it's barely playable, the game won't let me progress to the second level and if I died the screen stays black. I also tried the latest CVS but I don't think it fixed the problem.

I have been playing Tyrian 2000 (without sound) under DOSBox 0.63 with dynamic core and without problems. Using an AMD Duron 1.6Ghz.