Edit in JSFiddle

var WIDTH = 480;
var HEIGHT = 320;

var canvas = document.getElementById("game");
canvas.width = WIDTH;
canvas.height = HEIGHT;
var scene = canvas.getContext("2d");

Number.prototype.clamp = function(min, max) {
  return Math.min(Math.max(this, min), max);
};

var keydown = {
  states: {},
  left: function() { return this.states[37] || false; },
  right: function() { return this.states[39] || false; },
  up: function() { return this.states[38] || false; },
  down: function() { return this.states[40] || false; },
  space: function() { return this.states[32] || false; }
};
document.addEventListener("keydown", function (e) {
    keydown.states[e.keyCode] = true;
});
document.addEventListener("keyup", function (e) {
    keydown.states[e.keyCode] = false;
});

var Player = function(x, y) {
  this.x = x;
  this.y = y;
  this.width = 32;
  this.height = 32;
  this.color = "#0f0";
  this.draw = () => {
    scene.fillStyle = this.color;
    scene.fillRect(this.x,this.y,this.width,this.height);
  };
  this.shoot = () => {
    bullets.push(new Bullet(this.x+this.width/2, this.y));
  };
}

var Bullet = function(x, y) {
  this.x = x;
  this.y = y;
  this.radius = 1;
  this.vy = -5;
  this.draw = () => {
    scene.beginPath();
    scene.arc(this.x, this.y, this.radius, 0, 2 * Math.PI, false);
    scene.fillStyle = "#000";
    scene.fill();
  }
  this.isInBounds = () => {
    return this.y == this.y.clamp(0, HEIGHT);
  };
}

var Enemy = function() {
  this.x = WIDTH / 4 + Math.random() * WIDTH / 2;
  this.y = 0;
  this.vx = 0;
  this.vy = 1;
  this.width = 32;
  this.height = 32;
  this.age = Math.floor(Math.random() * 128);
  this.color = "#f00";
  this.active = true;
  this.draw = () => {
    scene.fillStyle = this.color;
    scene.fillRect(this.x,this.y,this.width,this.height);
  };
  this.step = () => {
    this.x += this.vx;
    this.y += this.vy;
    this.age++;
    this.vx = 3 * Math.sin(this.age * Math.PI / 64);
  };
  this.isInBounds = () => {
    return this.x == this.x.clamp(0, WIDTH) || this.y == this.y.clamp(0, HEIGHT);
  };
}

var player1 = new Player();
player1.x = WIDTH/2;
player1.y = HEIGHT-player1.height;

var bullets = [];
var enemies = [];

(function loop() {
  window.requestAnimationFrame(loop);
  step();
  draw();
})();

function step() {
  if(keydown.left())
  {
    player1.x -= 4;
  }
  else if(keydown.right())
  {
    player1.x += 4;
  }
  player1.x = player1.x.clamp(0, WIDTH-player1.width);
  bullets.forEach(bullet => {
    bullet.y+=bullet.vy;
    enemies.forEach(enemy => {
      if(bullet.x > enemy.x && bullet.x < enemy.x + enemy.width && bullet.y < enemy.y + enemy.height && bullet.y > enemy.y)
      {
        enemy.active = false;
      }
    })
  });
  bullets = bullets.filter(b => b.isInBounds());
  enemies.forEach(e => e.step());
  enemies = enemies.filter(e => e.active && e.isInBounds());
  if(keydown.space())
  {
    player1.shoot();
  }
  if(Math.random() < 0.05) {
    enemies.push(new Enemy());
  }
}

function draw() {
  scene.clearRect(0,0,WIDTH,HEIGHT);
  player1.draw();
  bullets.forEach(b => b.draw());
  enemies.forEach(e => e.draw());
}

<canvas id="game"></canvas>