Yes. Funny thing is I forgot to check back here and someone posted elsewhere about this system saying "anyone remember this" and specifically posted a screenshot of that game. So I came here to post I had the answer only to find out you already answered correctly. That game is fantastic. I hope I like the Irem arcade also.

I don't remember when, but maybe around 2007 - 2009 I went in Game Stop and they had a handheld retro game system for like $20 around Christmas. There were different ones.. one was Frogger and the other was generic light blue color and had maybe a 2.5 or 3 inch screen and I forget how many games in it.. 50? Something like that. It had a directional pad and I think 2 buttons. I wanna say they were both made by the same company.. could it have been Dreamgear? I don't remember.

Eventually I lost the battery cover and threw the system out, I regret that.

I don't remember any of the games on it (except one), some of them were pure crap, but the one I do remember as fuckin awesome. I've been trying to find it ever since.

So you're a princess. She walks back and fourth on the screen on her own. If she hit a block she climbs up and continues walking, however, if it was too high she would bump into it and turn around the other direction. Same thing happened that direction.. she'll climb up one block, but any higher than 1 and she bumps into and goes the other direction. Your goal was to put the blocks so she could climb up to reach the exit. I think there were fruit you could get for bonus points, but they were not needed to clear a level. There were enemies walking around later on I believe. But the real theat is water was rising up and you'd drown if you didn't get up and out in time.

I can kind of picture it in my head. Kind of NES style graphics. Screen did not scroll that I remember. Just static screens. The cool thing about this game is it had a bunch of levels, unlike a lot of games which only contain a few levels. I remember getting to I dunno 12 or 15th level once.