How does one get that rally car to do that run?

You must finish Arcade Championship in 1st position including the Extra Stage Lake Side on Normal difficulty to unlock it.

To choose it in Arcade Championship; on the car select, press left on the Celica MT for Stratos AT, or press right on the Delta MT for Stratos MT. 

There is no Special Car version of the Stratos.

Stratos rally run

Saturn185

Planetaryashes

Sega Rally Championship 1995

Desert

Sega Saturn

Arcade

T0pzu

computermachinemusic

roosetheroader

USA / NTSC

Fastest Lap (Standard)

Fastest Lap (Tuned)

Fastest Lap (Stratos)

Fastest Lap (Special)

2 Laps (Stratos)

2 Laps

3 Laps

5 Laps

Celica

Delta

1 Lap

3 Laps (Stratos)

4 Laps

3 Laps (Standard)

3 Laps (Tuned)

Stratos

Transmission

Time Attack

Mode

Practice (Forest)

Championship (Standard)

Championship (Special)

Championship (Stratos)

Practice (Desert)

Practice (Mountain)

Practice (Lake Side)

Sega Rally

Leaderboard Refresh - Jan 2022

Arcade Machine / Photo Submissions

Special Car

Discord

I see why you added emulation to the leader board, it should be its own separate category

Sega Rally Series - Discord Server

Brionac

Lonne

ULTRA_SALTY_DAN