The introductory level within a game is probably the most significant in terms of setting up the player to have a clear understanding not only of the theme but also simply how to play the game. Donkey Kong Country's first level is certainly no exception to the rule.
Let's jump in to the first thing you see:
On the first screen you are presented with three options: go left, go left and up, or go right. This already introduces players to the idea of exploring all opportunities, as well as a small introduction to the story. By going left the player will enter as Donkey Kong into his empty banana hoard: oh no, they're all gone! We must need to save them.... Upon exiting and climbing up (ding ding, another mechanic, climbing things!) the player enters Donkey Kong's tree house where they are introduced to two more mechanics, jumping on tires and collecting balloons to gain more lives.
The second screen brings two more mechanics: enemies and what I'll be calling monkey barrels. The player will use their newly learned jump skills to jump on the beaver, thus killing it. The player can then walk up to the shaking monkey barrel, and by masterfully mashing all the buttons they will find that one of them will pick up the barrel and throw it--and what a surprise: Diddy Kong!
The third screen confronts players with a floating letter "K", and upon collecting it players find out there are three more of these golden tokens floating around. After collecting the token and moving slightly right the player can see, just barely, a balloon beginning to float away over a tree. In this way the game uses an old mechanic, balloon collecting, to introduce a new one: being able to climb on top of the trees.
After this players can move right until they are confronted with new enemies. If they are playing as Diddy Kong they'll find that they can't kill these bigger enemies with him. After jumping over them they will find another monkey barrel and can retrieve Donkey Kong if possible, but they also find a new barrel which bursts when they walk through it. This is a checkpoint, although then player won't find out unless they die.

Guess what's on the next screen: that's right, yet another two mechanics! There is a vulture throwing stones protecting a floating golden ostrich token, as well as a plain brown barrel. The player will find that they can collect the token and pick up the barrel to throw when they want. If the player dies 2 times after this section, which presumably they will since they're a new player, then they'll find out they can continue to collect the floating ostrich token. Once they collect their third they'll get to become the ostrich and fly around to collect miniature versions of the token, receiving one life per hundred collected.


After this the player comes to a new item in the game: a box with a rhino head. Jumping on this box will release a friendly rhino, and if the player jumps on it they can ride it and it will automatically butt enemies out of the way. If the player also jumps too short over the gap--yet another mechanic, falling through gaps-- they might run into the wall which will introduce hidden caves. This particular cave holds lots of bananas and a balloon at the end.
Finally the player is confronted with one more gap and a sign signaling the exit of the game. Thus, the first level is complete and the player has learned most of the mechanics!
The pacing for this tutorial is fast enough to pick up the mechanics quickly, but set up well enough where the player won't feel overwhelmed by all of the new things they're learning. Nothing within this first level presents itself as a tutorial, and thus the player is left to their own wits to determine how to play. I personally find this to be a more natural process than a tutorial that feeds everything to you, making Donkey Kong's first level enjoyable and leaving the player wanting more.