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After searching around I can't seem to find any guide that details the triggers to enter the secret levels.

All I know of right now is that destroying the Moai head in Asteroids 1 takes you to ?Asteroid?, and that after one of the stationary sections there you get access to another secret level.

Anybody got a full list or more details?
This is from MGreen's FAQ over on GameFAQs:
raensi: Where are the secret levels?

BUBBLES: On Tyrian, you will meet a series of long ships which split up into
three parts as they fly; destroying these by shooting the front of them
reveals three coins. At one point, while encountering these ships, (I
believe it is at their second appearance) there will be a small rocky outcrop
on the VERY maximum right (scroll the screen). Destroying it will reveal a
small blue area; fly over this to access the Secret Level.
Before you warp into this secret level, I *strongly* recommend kitting
out your ship so that it can deliver a LOT of force into an enemy directly
in front of you. A plasma storm will help but may not, alone, be
sufficient, since it has low ammo. Contrary to my previous statement,
it is possible to get a good enough ship right from the start of the game,
but you need to concentrate on forward firing. Adam Williamson recommends
a level 4 sonic wave, level 3/4 multicannon, and mini-missiles.
When you enter the level, you will see why. Large lines of bubble
formations stretch right across the level; the one bubble in the
middle that is a different colour is the vulnerable spot. Shoot there
quickly; it is important that you destroy the lines rapidly, since if
you can't destroy the line fast enough, you'll fly into it.. and it's
strong enough to kill you in one. And since it's a secret level, there's
no second chance.
The good point of all this is: destroying one of those lines will get you
a big score bonus (and some odd bonus items - an Amiga tick? A pint of
beer?). Even better, just beyond the lines lies a huge area of free coins,
just lying there! For this reason, if you get an Attractor later on, a
visit here is highly recommended! Watch out though, and do keep shooting -
there are some hidden bubbles in the layout that will damage you if you hit
them while you're collecting coins. On harder levels, they will also
generate smaller, moving bubbles. But if you destroy the large bubbles,
they'll turn into gems! There are a couple more of those nasty lines before
you leave the level.

WINDY: If you are playing on "Hard" level, or higher, you use the above
method to get to "Bubbles", and you are playing v1.1, you will not go to
"Bubbles"; you'll go to "Windy" instead. Windy has the background of
Tyrian a maze-like map similar to Soh Jin. Certain walls are marked with
dollar signs or other symbols; destroying these will reveal bonuses.
However, there are also mean turrets mounted on some walls!

HOLES: Immediately after the computer voice on Tyrian says "Danger", and the
screen displays "Approaching enemy platforms", a wave of circular ships enters
on the left. Kill the leader, then kill the one at the very back of the wave.
The one at the very back should drop an orb when he dies.
The actual key to this is *not* that only those two ships should be
destroyed, but that you must destroy at least two ships, including the last
one, *in order*. Even one hit with a weapon on an enemy out of sequence
(even if it does not kill said enemy) will disqualify the orb. The above is
just the simplest way of achieving that.
Holes is a long and difficult level. The enemies are similar to those
encountered on Tyrian. Be warned - there are several places where a clone
of the Tyrian boss will pass you, firing considerably more densely than
the original one did!
By the way, on both "Holes" and "Bubbles" you can find a data cube which,
when collected, will contain a message from Steffan of OMF2097. Another
one has been found on "Holes" which seems to be an advert for Jazz..

SOH JIN: If I had a penny for every message I've recieved about how to get
here, I would be a rich man. This method works 100% for me: At the very
start of Tyrian, you are attacked by a wave of U-fighters. Do not destroy
any of these fighters (except for the leader to get your powerup pod - see
the seperate section.)
Later, after you fly through the spikes, you are attacked by several waves
of small ships, followed by a wave of five ships heading across the screen
travelling at different speeds. There will be a second ship behind the one
in the centre. Shoot it to reveal a glowing sphere, and pick it up for the
secret level.
Soh Jin is a maze of walls and turrets. The walls are very dangerous -
flying into one will severely drain your shield. There are no mobile enemies
on the stage, apart from the Help Ship. You'll see odd objects, resembling
keys, lying around on the floor in this stage. Each is worth 500 points!
Also, unusually, you can retry Soh Jin until you get it right.
Even more usefully.. in Arcade Mode, destroying the turrets on Soh
Jin gets you weapon pods. In Full Game mode, check out the upgrade ship
menu right BEFORE you battle at Soh Jin. There are several weapons, and
a powerful (and expensive!) shield, available there that are not available
anywhere else.
SILLY CHALLENGE: There's no award for doing it, but if you fancy a
challenge, try this: Fly through Soh Jin without ever firing a shot. It's
possible, but rather difficult. Your shield will be up a lot of the time,
but if your armour gets low, watch out.. 'cos you'd have to fire to destroy
the help ship!

ASTEROID?: On Asteroid 1, there is a small platform with a face on it.
Destroy this face to reveal the orb.

MINEMAZE: On Asteroid 2, there is a place where there are three faces on a
platform arranged like this: ,', . Destroying the one on the maximum right
will reveal the orb.

THE INTER-SECRET WARP: You can move directly from "MINEMAZE" to "ASTEROID?".
Here's how (info from Vincent Torre): At one point in "MINEMAZE" there
is a stage where five strawberries fly down the screen, down a
small channel. The snag is, this channel is bracketed on the left and
right by one-way magnetic barriers that allow you - indeed, try and force
you - to fly out of the channel, but won't let you into it.
Get the strawberries if you can then head out of the channel, across the
barriers, on the left. Do NOT rejoin the main path of the level - stay on
the left even when the gate/door and the new set of one-way barriers comes
in on your right, and you will fly up a small passage on the left of the main
level. WARNING: Do NOT fly back over to the right! The barriers will
render you unable to fly back left and hence unable to get the secret. You
will meet a series of small ships that swing back and forth at the top of the
screen, dropping missiles as they go. I believe that either the third of
these, or the ship directly after it, holds the orb.

MISTAKES: In Ast. City (episode 2) you will be attacked by ships that fire a
lot of shots in a wide spread. They look like regular enemies except for
their red gun turrets. If you destroy all of these enemies, you will find
the secret level floating on the right side of the screen.

TYRIAN-X, SAVARA-Y, NEW DELI: These secret levels appear automatically
after you finish the third episode on Hard difficulty or higher. I strongly
encourage you to go for this - they are very nice levels; a lot of the
data available on them is very funny, New Deli reveals something you
probably didn't know about the game interface, and the music on the first
bit of Savara-Y is the best in the game (Imho) - it's so good I almost
didn't want to fire over it... ;)

GEM WAR: On the level "Gyges", just before the first wave of claw ships,
there is a small pod. Shoot it. This same pod occours three times during
the level - once just after the speedup has finished, and once later on.
Destroy all three pods to get the orb.
dpezet: /snip
Thank you. For some reason I only checked the FAQs for Tyrian 2000, thinking there would be the same ones for both the original and this one.

+1 for your help