For a lot of the emeralds in both 1 and 2 you kind of just had to know or discover by sheer luck. In Sonic 2 for example there's a sky level where in order to reach the emerald you had to get to a spring board hidden in a specific cloud (of which there were many) and if you missed it you fell to your death.
The Sonic 2 Chaos Emeralds were so
Devilishly evil I love it
Underground Zone - Blind jumps from spring to spring with lava all around, Not bad really
Sky High Zone - Either find the hidden spring in the cloud or learn how to hang glide like a pro (I did the latter because I didn't even know that spring existed until recently)
Aqua Lake Zone - As your zipping along a blind pipe system you have a choice, Left or Right, you'd better pick correctly as you can't get back in the pipe (This came back as a Sonic Chaos Special Stage)
Green Hills Zone - A return of the blind spring jumps from Underground Zone, except this time you can go too fast and completely overshoot the platform its on and won't even realize it was there at all
Gimmick Mountain Zone - Blindly jump at a random specific wall that has no collision and no indication that you can even jump through it
Scrambled Egg Zone - Beat Silver Sonic with all 6 Emeralds, if you missed any from the previous zones you don't get it so you end up thinking it's in the previous level somewhere except it's not, good luck searching the hardest level in the game for it over and over again for no reason