A short Robotron 2084 strategy guide by evilkalla :

As you play more and more Robotron there are some subtle strategies that will allow you to progress father and die less often with some degree of consistency. As I've played the game myself, I've come across some hints that I think will really help you kick lots of robot ass.

1. Know your surroundings

When the wave begins, you'll notice that you have about two seconds to "take in" your surroundings before the evil baddies come after you. This allows you time to formulate your plan of attack before you begin combat. Typically you should use this time to figure out a way to get into an open space, away from the grunt Robotrons. Failure to do this is what leads to sudden death at the start of many waves. Don't get too mad if you lose a life or two; sometimes a level sets up in a way that it's impossible not to. Electrodes play a big role in choosing a path. There might not be any grunts in one direction, but a wall of electrodes instead.

2. Kill the quarks!

On levels containing quarks, you should make it a point to get rid of them quickly. Ignore the humans completely unless they are right in your path. Quarks spit out lots and lots of tanks, and if more than five or six of them get on the screen at once you're going to have a hard time not dying.

3. Kill the sphereoids!

Make it a point to kill the sphereoids first. Though there may only be two or three on the screen (more appear as the waves progress), they create lots of those enforcer bots that, just like the tanks, will kill your ass really quick. Note that the sphereoids tend to stagger in their trajectory kind of randomly, so don't get too close. They might fly right into you and that's -1 life right there.

4. Know the brain levels!

This is your chance to clean house. You get a chance to scoop up lots of points killing brains and lots of point grabbing humans. But, be careful, since the brains are constantly spitting out those cruise missiles, and these can be pretty hard to hit, especially when they travel diagonally. Typically I make it my point to get as many humans as I can. You can get so many of them that you will more than likely get a lot of 5000 point bonuses right after one another, and they add up to 25000 point free men fairly quick. You can get 2-3 free men on a brain wave if you play it right.

Additional user notes:

Simply, the brains (and this is a bug) all go after mikey first. Once he's progged they take off after everyone else. Use those couple of seconds of breathing space to locate mikey then expend all your effort killing brains heading towards him and you (they'll just be on the way to mikey). Keep him alive and eliminate the baddies and you'll have a room full of humans. yum!

The Brain screens are sequential, based on groups of 20 (actually all board combos are based on 20):

5, 25, 45 etc. - Mommy screen (brains go for Mikey.)
10, 30, 50 etc. - Daddy screen (brains go for Daddy)
15, 35, 55 etc. - Mikey screen - the hardest IMHO (Looking for Mikey, again.)
20, 40, 60 etc. - Family screen - (not too sure, but I think it's Daddy.)

At the start of ALL brain waves (not just wave 5), the brains search for one particular human. When that one is changed to a prog, then the brains are released to kill at hearts content. When the wave starts, all the brains will turn and move towards the one that they have to get first, so if you can zero in on it; keep it alive and unrescued for as long as possible.

Other 20 wave qroupings:

Tanks in regular screens: waves 27-40, 47-60, 67-80, etc ...
Tanks and Spheroids exclusively: 24, 44, 64, etc...

Tank waves:

If the tanks shoot 20 shots in a row, without you killing a single one (shot, not tank) they will not shoot anymore. Of course, once you fire and hit a tank "bullet" it resets back to 0 shots fired and starts all over again. I think the limit was put in the original to save computing power (too many things on the screen) and it was faithfully transferred to Williams Arcade Classics. Don't worry about humanity on these waves, just save your own butt.

Another tip: the closer you are to a shooting tank, the slower the shot moves. This sets up an interesting strategy where it is sometimes better to move in the middle to slow the shots, and then break for the outside, shooting in. Fast angle tank shots are the supreme killer on this wave, as you well know. Keep out of the corners!

Spheroids:

These suckers aim at you in the beginning of many waves - I've seen a number do 90 degree turns just to run into me. If you destroy a spheroid and ALL the enforcers that it has released, that spheroid will not (usually) reappear if you die. This hint works most of the time and is a good general rule. Quarks, which generate tanks, stay dead.

Limits:

Due to the 8 bit processor, the machine could only count up to 255. Once it hit 256, it "rolled over" to 0. This causes some interesting and frustrating things to happen:

1. Once you hit wave 256, you started again on wave 1.
2. If you get 255 extra men, and you reach that 256th extra man, the machine will roll over and give you 0 extra men. You still have the man you're playing. I lost two 25,000,000 point (6 hours each) games this way. Both times I was going for the record of, at that time, 100,000,000 points. I was quite pissed. I later rationalized it as giving the machine such a butt-whupping, that it quit. Rolling over your men is as close to beating Robotron as you can get.

note : borrowed from and adapted from my own web page, http://www.tripoint.org/robo/robotron.html