It's certainly not difficult to tell this game is beta! The graphics are awful (especially the polar bear, apparently drawn in Microsoft Paint), the music uninspired, the controls unresponsive, and the game balance non-existent.
For whatever reason, people keep offering IQ-crushingly banal tips like, and I only lightly paraphrase, "To beat the polar bear, you need to shoot it lots until it dies!" and "Try to avoid the spikes, dogs [sp], and snowball machines because they kill you!" Way to illuminate the blindingly obvious, assholes.
To beat the polar bear, fall onto the first ledge, butt up against the left wall, face right, and wait for the bear to walk over the jump pad at the far bottom right. When it's there, tap shift a few times to hurl some low-aimed snowballs at it. You need to tap it--if you hold down shift you'll aim all over the place and waste ammo. Even still, you may run out of ammo and have to suicide to restock (beta!), but eventually the bear will go down. It's very boring, but it works every time and is not at all risky.
The final boss is really poorly designed. Even when you know what to do, most of the time you'll lose because there's no way to protect yourself from its beam, which it fires at random intervals and random distances.
First, note the icicle above the beast's head. What you want to do is keep jumping and tapping shift, trying to hit that icicle. Once hit, it'll fall and hit the beast. The icicle will reform several times; keep hitting it until it stays gone. If you're really lucky, you can pull this off without loss of life. Most of the time, you'll get killed once or twice no matter what you do (beta!).
Once the icicle stops growing back, try to get down to the bottom of screen. Despite what the jerks here would lead you to believe, it's not "just that easy." Most of the time, you'll get zapped and die on the way down, and there's simply nothing you can do about it. If you do manage to get down there, get under the floating platform. Notice that the beast has two phases of arm movement it alternates between--one slow that sweeps the top half of the screen, and one fast that sweeps the entire screen. During the fast, full-screen sweep, what you want to do is jump as the beast's arm starts passing into the bottom half the screen, and blast its face with snowballs. If it works, he'll flinch in pain, same as when you hit him with the icicles.