Crystal Mines 2, Lynx
Ah, sweet satisfaction.
My brothers and I got Lynxes as Christmas presents back when Lynx's existed. Although the Lynx is now known as a failed system, I know that I never thought of it that way--if there weren't very many good Lynx games, I spent hours playing the ones I did own, Shadow of the Beast, Todd's Adventures In Slime World, Junk Yard Dog, and Crystal Mines 2. Especially Crystal Mines 2.
This remains one of my top puzzle games of all time, and I really feel that if it hadn't been exclusive to a doomed handheld system, it would be fondly remembered. You play as a robot (or rather, you are *cough* "controlling a robot with your Lynx Robot Controller") from a top-down perspective in a 2-D plane. Your goal is to collect a certain amount of treasure and then reach the exit which will then appear. Your robot has very limited controls--you can shoot, you can use bombs that you collect, which will destroy some things your shots cannot, and you can push boulders. You can also self-destruct if you have rendered the level impossible. Your robot is highly delicate for a mining machine; one hit from any of the monsters wandering around the mine will kill you, being crushed by a boulder will kill you, as will a number of other things that you discover as you press onward.
At the start, this game is completely straightforward; you're in a level full of dirt and a few basic monsters. Blast your way through dirt and monsters, grab the treasure, leave. But it quickly amps up: explosive blocks, radioactive blocks that will "poison" and quickly (in a few seconds) destroy your robot if you touch them (unless you find a curing item in time), red slime that spreads slowly through the level and will kill your robot if you get stuck in it, but which turns into crystals if you bomb it twice; one-way gates, gravity changing mechanics, holes that will swallow your robot or any gems that fall into them, one-way gates, golden pipes that turn rocks into gems and gems into rocks colored rocks that fell upwards or downard depending on their color, which could be changed by shooting them, and a lot more.
So I played this game a lot as a kid, and got quite far. But I never beat it, and I made full-use of the level-skip option that the game provides if you keep failing ("You seem to be having trouble. Press A to skip this level. Press B to take more punishment). On and off I tried again in later life I came back to it, starting at the first level and trying to conquer, and eventually getting stuck each time. I mean, I don't want to make it seem like this was some kind of life-long obsession; years would go by without my playing Crystal Mines 2. But it was a game I loved and never managed to beat, which remained at the back of my head.
Well, some time ago I began my last attempt. I got quite far (into the 130's or 140's out of 150 levels) before being stopped dead. I spent weeks failing to beat the same level, and gave up. Came back months later, beat that level (still the only level I remember thinking was unfair in its design), progressed a little, hit another wall. Struggled, put the game down, came back later, conquered. And from there, it was a pretty straightforward path to victory. The last level was challenging and satisfying, but only took me a few hours compared to the two road-blocks that almost ruined this run.
This game was actually ported/remade for both the PSP and the NDS, but it may never have been released in the states and is in any event long out of print, with a aingle used NDS version on sale at Amazon for a hundred bucks. If you like puzzle games, and if you don't see a problem with emulating the console equivalent of abandonware (which I don't, but different stroked and all that) then I recommend it.