These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Crowning Music of Awesome: The music of the very first level, "Tyrian", the battle music against the green ship, "Deli Shop Quartet", the music of the first level of Episode 4, "Rock Garden", and many more. The game's SETUP and SHIPEDIT programs have a "Jukebox" mode where you can just sit back and listen to the music.
Demonic Spiders: The green platform-like ships in the Deliani levels. They come in threes, fire at quite a fast rate and take forever to die. On the higher difficulty levels, nearly every enemy becomes a Demonic Spider, especially in Super Arcade Mode and Super Tyrian where you have no rear gun and crappy shields.
To give you an idea of how bad the green platforms are on higher difficulties, even the almighty SDF Main Gun will take several shots to kill one of them.
Ear Worm: Most of the music in the game, although the music from the very first level deserves special mention.
Game Breaker: Penetration weapons, such as the Mega Cannon and Zica Flamethrower may not seem all that powerful, until you realize that you can "affect" many enemies, including bosses, with them and One-Hit Kill a lot of them by ramming your ship into them. You should die from doing this in a realistic sense, but you don't.
Penetration weapons are nasty enough, but in a secret level of Episode 4, you can find a Wave Motion Gun on steroids, the obscene "SDF Main Gun". It combines penetration into a huge blue laser the width of your entire ship! On top of a Front Laser/Zica Laser, you'll obliterate anything not flagged as invulnerable.
Any ship that allows you to convert your shields into armor makes survival of all but most intense levels a breeze. If used at the most opportune time, you can never run low on armor. In fact, you can often abandon the more expensive ships in favor of a "Gencore Maelstorm" just because it can refill it's armor with an easy Twiddle Command, something the late-game "Stalker III", and lesser "Gencore Phoenix" can accomplish as well.
Good Bad Bugs: If you activate the invincibility cheat in story mode, quit, and then start a game in one of the arcade modes or Super Tyrian (which disables cheat codes), you'll still be invincible as long as you don't press any keys during levels. You can still play the game with the mouse.
Nightmare Fuel: "Eyespy" is filled with disembodied body parts, especially eyes. That fact that they can spawn smaller wriggling eyes doesn't help a bit.
Savara V in Episode 1. You know those waves and waves of ships and blimps that you can casually mow through with your guns? Read the data cubes before the level start, and you will discover that they're all full of civilians fleeing from the boss of the level.
Not only that, but in Arcade Mode, the blimps are an essential source of weapon powerups. They easily drop a half-dozen or more apiece.
Episode 1 ending. If not, things could become unpleasant.
Seasonal Rot: Episode 5, included in Tyrian 2000. A good number of players consider it to be this as it is very short, contains no new music, the new weapons and ships are no match for the stuff that the first four episodes have to offer, and much of the artwork was not done by Daniel Cook, the original sprite artist for Tyrian.
Due to technical reasons differences in the data file structure, the OpenTyrian source port ends at episode four. Development of a version that works with all five episodes seems to have become Vaporware, possibly due to lack of demand.
Soh Jin, a secret level in the first episode had destructible "red blocks" that did massive Collision Damage if you bumped into them. Also, unlike many other bonus levels where you exit the level if you got killed, this one forces you to complete it without dying...
Windy, another secret level in Episode 1 that contained the red blocks from Soh Jin, except this time they were indestructible and were accompanied by stationary orange blocks that fired very damaging blue spheres at your ship and pushed you into them...
The first bonus level in Episode 3 (also Deliani-themed, go figure). Aside from the aforementioned green platform ships, it also featured barriers of indestructible orange rings. Most of them move, some of them move very fast, and a couple of sections of the level have walls made of them, with just enough space between the rings for the sonic wave shooters on the other side to fire in at you while large green orbs (fortunately destructible) flew around and forced you to stay on the bottom of the screen. If you don't have side-firing weaponry and/or the Repulsor ability, you'll be dead several times before you can say "Oh crap I died".
This is even worse in the arcade modes. In story mode if you die in a bonus level you just move on to the next level with no penalty. In arcade mode you lose a life - and a level of weapon power - until you run out of lives, then you go to the next level ... with a low-power weapon and no backup lives.