What to do on each level
One thing to know first: the game itself has no continues and no checkpoints. Die without an emulator save state and you go back to the SEGA logo, the Virgin logo, the title screen, and the story crawl — roughly twenty seconds of boot screens before you can play again. Save states in the browser fix that, so use them before every T-800 encounter and before planting the reactor detonator. Easy mode hands you a Uzi-9mm in level 1 that turns the whole opening into a shooting gallery; Normal and above strip it out and stretch the gaps between health drops, so the harder you crank it, the more "unavoidable hit" becomes a real category of damage rather than just bad play.
Level 1: destroy the reactor
Grab timed detonators from the spawn point near the entrance. They respawn forever from that spot, so refill any time you pass it; you can carry nine, and one detonator clears every Hunter-Killer on screen at the moment it goes off. The first Armored Tank goes down to grenades, but stand directly under the cannon and it can't hit you. Down the first ladder, head bottom-left to find the rifle, which replaces grenades and gives you continuous fire for the rest of the level. Detonate the wall blocking the path forward. Past the row of three gas tanks (the landmark you'll want on the way back) is another wall and the huge red reactor behind it. Plant a detonator next to it. The screen turns red. You now have 45 seconds to retrace your steps to those gas tanks, up the stairs, jump right, climb the ladder, and reach the time machine. Ignore the parachute bombs from the aircraft on the way out. There isn't time.
Level 2: rooftops to TechNoir
You arrive in 1984 with a shotgun, which is now your only weapon for the rest of the game. The street is dense with cops (who can't be killed, only stunned) and punks throwing molotovs (who can). The smart play is to skip most of it: climb the first set of ladders, stay on the rooftops as far as they take you, then drop down near the end and deal with whatever stands between you and the phone box. Climb the beams onto the building rooftop and walk into TechNoir. The helicopter that buzzes you up there can't be destroyed and can't reliably hit you, so just keep moving.
Level 3: escape the police station
Looks maze-like, isn't. The geometry funnels you in the right direction whether you notice or not: left, up the stairs, right, up the stairs, left, up the stairs, ladder to the roof, then right, down the ladders, and left to the corridor where the T-800 is waiting. Getting flanked is what kills most attempts here, not getting lost. Clear any cops or prisoners around you before you start trading shots with the Terminator. Two enemies hitting you from opposite sides is how most attempts end at this point.
Level 4: the compactor
Only one enemy: the endoskeleton, dragging one leg, fast. The shotgun knocks him backwards but cannot kill him, so the whole level is a herding problem. Up the stairs so he's below you, up the ladder, push him back twice with shotgun blasts, down the ladders, right, up, push, down, ladder, right, up, ladder, right, push, ladder. Eventually he's reduced to a torso pulling itself along the floor, and even then he can't be jumped over. Lead him the last stretch to where Sarah is. The compactor does the rest.
How do you kill the T-800? You don't.
The first time you meet the Terminator in TechNoir, you can dump shotgun shells into him for what feels like a full minute and watch his health bar do nothing. He doesn't have one. He has a stun counter. Hit him enough times to knock him down, wait for him to get back up, knock him down again, then a third time. After that third stun his body starts blinking. That's your window to run past him. The blink doesn't last long, so commit to it the second it starts.
The technique that makes this possible is crouching while firing. Standing up, Kyle does a slow draw animation pulling the shotgun out of his coat, and that draw alone is usually enough to get you killed against the T-800. From a crouch, he skips it. Your fire rate goes up. Fewer shots connect. When the T-800 drops, back up a step. He'll get up where he was. Crouch and shoot him down again. Repeat until he blinks, then go.
It's the same fight in level 3 with one extra problem: you're in a building full of cops and prisoners who don't care that you're busy with a more interesting enemy. If even one of them is shooting at you from the opposite side while you're trading hits with the T-800, you'll lose. Sweep the room first. He doesn't go anywhere until you give him a reason to.
Two rules Kyle never breaks
Don't let enemies touch you. Direct contact drains the energy bar fast, and on harder difficulties, where health bottles are scarce, that's how a clear stretch turns into a save state reload. The Hunter-Killers in level 1 respawn forever, so clearing the room isn't a goal. Keep walking right after each kill, never standing still long enough for a fresh one to reach you.
Don't fight on stairs. If an enemy is somewhere on the same staircase as you, pull back down and wait for them to leave the steps before you start shooting. Stair geometry pushes them straight into Kyle as they walk, which is contact damage on top of bullet damage and the worst position to be in. Drop off, fire from flat ground, then advance. Try it online in the browser and the rule explains itself the first time you ignore it in the police station's stair maze.