Ice Mountain
Upon completing the mine, revisit the Ice Mountain on your world map. When you cleared this area previously, you pushed a block into a structure in the ruins at the last area. The path here is unchanged, so return to this area to trigger a new cutscene.
Fire Mountain
Return to Fire Mountain and take the path you cleared earlier in the game. The last time you were here, a platform appeared after you defeated the boss. Jump on this platform once again to reach the ruins. After you walk up to the structure, a scene will play and the Gate will open on your world map.
Gate
Travel to the Gate on your world map. After watching the story scenes, walk into the bridge to begin the Gate dungeon. Like most previous dungeons, you will have to overcome a series of battles and puzzles to continue through the game. At the end of the Gate you will fight a gold and a silver robot. Target the more dangerous silver robot first with your normal attacks. After the robots are defeated, the path will open to enter the Tower.
Tower
Once inside the tower, you will run into puzzles involving pools of water and blue and red barrels. You can use the blue barrels to freeze water and the red barrels to destroy certain blocks or to melt ice. The tower is quite long and offers you plenty of puzzles and enemies before you reach the end. When fighting the final boss's first phase, damage the smaller monsters until they explode. If the boss is nearby, the explosion will stun him and allow you to deal damage until he recovers. Keep repeating this cycle until the boss is dead. He then reappears in a much harder second form. Target and destroy the spell-casting magic pillars as well as the boss's arms to reduce the amount of incoming damage. With only the boss's main body remaining, keep attacking him until he is defeated to beat the game.