Just some thoughts based on observations:

1. The closer you are to the top of the screen, it appears like it takes less time to clear the the level after beating the boss. You seem to see the text faster.

2. This is fairly logical, but weapons that are fixed and do piercing damage per tick (like the SDF Cannon, Plasma Storm, and other side kicks and specials) appear to do their damage quicker when you're closer to the top of the screen.

I'll report back if I prove these.

So yeah, both of these things do save time.

Tyrian is a pretty unique game in that it has a common TAS and speed runners tool built right in. You can frame step with one of the cheat codes - Num Lock + Backspace. This is how I tested.

Tyrian looks like it runs at 30 frames per second. On average, being close to the boss saves about 10 frames, and being close to the top of the screen seems to save 8-10 frames.

On top of all of that, Plasma Storm is definitely the fastest way to kill a boss due to piercing and it's rather unique instant deploy. I'd thought the game skipped ahead, but with some further testing it turns out that you can literally deploy all of the plasma on single frames, so it looks like 6 frames in total. The game doesn't appear to know how to handle that with the pause cheat so it just acts as if they were all deployed on the first frame.

You should also be able to get a quick kill on the first boss (AKA, kill it without leaving the top part of the boss behind to finish off) if you wait for it's firing noise every time. Whether this actually saves a huge amount of time is doubtful though, as, I'm guessing the boss is vulnerable shortly before that. It might actually be faster to just use the close range and top screen warp time saves and not really care about this.

If executed well, you might save about a minute over the course of the 30 levels with bosses where this is applicable, but obviously some level layouts might make this unsafe to do.

Here's the video:

I also test out how many frames it takes for the SDF to fire of the screen and recharge, and for the Plamsa to be off the screen. And in case you were wondering how many frames it takes to get full shields, and out of invulnerability, that's in there as well. Spoilers, it's about 100 and 200 frames respectively.

FYI, Tyrian actually runs at 35 frames per second on Turbo according to Gamfaq's -nic who has been going through the OpenTyrian source code here: https://gamefaqs.gamespot.com/pc/564490-tyrian/faqs/75999/what-is-this-guide

So this is a little bit less of a time save, but not by much. Probably a 40 to 50 second time save if executed really well.

Check out the guide's info! There's some interesting stuff there. Not much that isn't already obvious, but at least there's numbers to back things up now!

I keep revising this, damn.

So in my testing with the debug cheat, Tyrian runs at 47-48 FPS in Turbo.

Long story short on the testing:

1. Tyrian runs at 47-48 FPS in turbo, not 35 FPS. Weirdly enough, this is seemingly confirmed by Jason Emery himself in this thread that I didn't notice till now: https://www.gog.com/forum/tyrian_2000/how_to_get_60fps

2. Playing with fixed CPU cycles does not increase the FPS, no matter how high or low you go. It does eventually slow down the game and cause various sound issues though!

3. Playing with Ctrl + F12's 5% CPU overclock on the normal MAX setting in DOSBOX does nothing to FPS.

4. There's little time difference in killing the first boss quick or leaving the top behind.

5. Detail settings don't affect FPS.

Here's the Video:

Takeaways:

1. Kill Bosses any way you like for speed.
2. Play any detail setting you want - no affect on speed.
3. Changing the dosbox CPU game settings does not affect FPS positively.
4. The FPS is 47-48 on turbo. so close range kills and the top screen warp are at most a 20-30 second time save. This also explains some of the weird inconsistent frame counts on certain specials, and my odd screen tearing and sound issues that I don't see on real DOS with a CRT. Basically my 7 year old monitor sucks and can't stay in sync to such an odd value.
5. There's a lot of menuing and screen transitions in this game! Probably at least 4.5 minutes worth. If there ever was a Menu% category, it would likely be the least fun cat.