I am the first person to complete Icy Cave of Frustration! This is as far as I know and legitimately. I did it some hours ago. I still need two medals tough. It took several hours per day for a month (and some acceptable cheating). I disagree with the medals, I'll try to convince the author to change them. After all, I'm the only one who has completed the game and I'm a medal hunter, so who better than me to say that the amount of points you get is miserable.
Some tips - don't read if you are not interested in the game
There is a guide but it's a bad one that doesn't help. I will not write one. Commit yourself to the game. I guess if you play long enough you could get there. The medals are not worth it.
I got a few screenshots of the last levels, the links point to them. Not really helpful but anyway. Spoilers ahead I suppose. There are 20 basic levels and 5 special ones. There is not much difference between them. Special levels are not numbered. Level 17 by the way is at the moment numbered 18 by mistake.
I find levels 18, 19 and 20 to be of reasonable difficulty. 21 is hard. It has one of the fastest caveman, strong wind and birds. Level 22 is what I consider to be hardest level. It has a deadly combination of a small icicle and a fast caveman. It requires precision. Don't worry about the birds. Birds (in all levels where you find them) fly slightly upwards. If you wait long enough they go out of screen, posing no treat. It takes too much time, so it is not efficient to wait, except here in 22. Level 23 has one of the reasons for why I requested an option to expand the game screen (top right orange buttons). Tiny cavemen. Making the game screen bigger will let you be more precise. This level has slow cavemen and a big icicle so it's easy. Drop it when the slowest caveman is under the icicle. Kind of like in the screenshot. I beat level 24 using experience from previous levels. There's not much about it which is why I got no screenshot. It is kind of hard. Finally level 25. Do you still have doubts about how easy it is LiquidOoze?
As for cheating, I'm not even sure if it is cheating, it's more like a trick or a strategy, I'm not sharing! This game got me so mad that I will keep the trick I used for myself. Sorry about that. Remember that practising goes above all, so you would still have a lot of work even with the trick, which you can figure out by yourself... DiMono has a trick that he posted here, it has a few similarities, but mine is much more advanced and better :P
Have fun. Oh wait, that's not possible with this game :(