Tomb Raider I-III Remastered Starring Lara Croft

There are lots of places for this achievement, but it can also be done in the second part of the very first level, The Great Wall.
When you open up the door to the outside area of the level, where the crows are, kill them and run to the other side of that same area (where the door and keyhole are).
When you arrive at the door, climb the right area to see a green path and some slopes.
Jump there, taking care to not fall on the slopes so you don't slide down the path.
Follow the green path around the area with the lake, and go up the first Guardhouse.
On this Guardhouse you can get 3 achievements: "10/10", "20/10" and "Crane Dive".

Go to the edge near the lake walking slowly, press down to make some space to the jump, run and jump holding RB (the swan dive). During this dive, you need to keep pressing ROLL (B) to make a somersault (you can also get the double somersault if you are fast enough).

Video:

Playing the game normally without level skips, the first time you can do this is after killing 3 crows just after your first climb.

Stand in this spot and Save



Hold and Jump Forward
Hold

Lara will Dive and Somersault once.

Tomb Raider II - The Great Wall (Level 1)

You will make your way to an outside section between two guardhouse towers, with a steep drop to your right and a pool at the bottom. Your destination is the top of the guardhouse behind you (where you came from). Make a jump off the right side higher wall ledge to the green/foliage slope ahead to the right. Use classic graphics if needed and progress to the right and around back towards the first guardhouse, making sure not to step on steeper ledges that will drop you down below. You have to make a lined up running jump at the first corner, then at the second corner you can do another to leap up a level. Just before the end of this highest ledge you can make a running jump and grab to the guardhouse roof.

Make a save and line up on the right side roof ledge, aimed at the pool below. Do a running swan dive (push forward + Walk and Jump once you reach the ledge on Tank Controls) into the pool and mash the Roll button as you jump/fall. If you do it right you will barely start a second somersault before hitting the water but it should count and you'll get 3 achievements total.




Video:

Playing the game normally without level skips, the first time you can do this is after killing 3 crows just after your first climb.

Stand in this spot and Save



Hold and Jump Forward
Hold

Lara will Dive and Somersault once.