Note: The screen presented here is from the Atari 5200 and Atari 800 versions of the game. If you are playing the game on a different system, some of the points mentioned below may not apply.
Advanced Teleporters has the most complex layout of islands compared to any other stage. As such, there is no one direct route through the stage, but rather a collection of isolated regions that must be covered indepedantly in any order. This stage will test your ability to rely on rather small sized floating platforms. In order to make many of the jumps from one island to another, you are required to stand on the opposite end of the island before you jump towards the next one. The BF situated at the top of the screen stands for Big Five, the software house responsible for Miner 2049er, and is worth the most points out of any item in the game, 1100.
The strategy proposed here is just one possible route through the stage. Start by teleporting to station 4. Make sure you are on the left side of the teleporter or you may be forced to use the slide. Complete that island and wait for the floating platform to pick you up. Use it collect the BF, and use it collect the happy mutant beneath you, and clear that island and the one beneath it. Then get back on board the floaring platform and ride it to the right. Clear the large island with the two slides attached to it, and take the left slide down. Once on the floor, use the plunger to clear the mutants down there and teleport to station 2 to clear that mutant as well and finish the framework. Use the floating platform to reach the islands to the right. Jump over the iron and to the platform on the right, and drop down to the one below it to clear the islands before dropping to the floor. Then clear the two lowest platforms. Work your way to the series of islands along the right side of the stage, and back towards the island beneath the Anvil. Clear as much of it as you can and slide back down to the floor. Then teleport to station 3 to clear that framework, and carefully use the floating platform to finish the left side of the platform to the right.