I'll explain where the various optimizations come when NOT using tails, using the in game timer from the run you linked to.
First, to start, you can spindash jump off that slope and carry enough speed to take you through that area slightly faster (about 1 second saved).
At :23, instead of holding right to slow down like i did to manipulate tails like i did, you can save some time by letting your momentum carry you through the to the area with the yellow bumpers.
At :34, you can jump a lot sooner than that, land on the platform, and THEN hit the switch (not jump to the switch like i did).
At :45, you can spindash instead of running which is what I did, to save another half second.
At :53, I wait way too long to spindash on those platforms. Watch the knuckles vid of how to properly spindash-jump through this area with the spike-blocks, as it was really slow in my vid.
At :58, you do not need to charge up a huge spindash like I did, you can do it a lot quicker.
At 1:00, you can roll down that area instead of standing, which saves a bit of time because you are rolling down the slope.
1:05 is actually possible without tails, believe it or not, but you have to perform this pretty well. That vid has a lot of my older strat's (as you can see by some of the various optimizations that apply to both sonic alone and sonic with tails), and I think 1:01 is doable with tails.
Actually a lot of the metropolis levels have more optimizations now that I look at them that are not used. My 2:02 for metro 3 is good, but its so much better than the others that I didn't bother optimizing it to death.