With this, you can expect a completed run under three minutes within' 25-75 attempts. (depends on skill)

1-1:

Run until you come towards the first pipe. Enter it. Try to exit at a time ending with a 6 so you don't get fireworks. When going on the stairs, try not to hit into the two "hidden" blocks so you don't lose time.

1-2:

Run until you encounter the third pipe, enter it and exit at 2 or 4. This will make you not get fireworks. When going on the stairs, jump on the last time before the top of the staircase since there is a red koopa on top that can kill you. When it moves to the right, you may proceed.

1-3:

Try to quickly use the two "hidden" blocks at the beginning to skip the underground portion. In the overworld portion, try to use the "hidden" blocks instead of trampolines as they're way safer.

1-4:

Turn left before falling the second time and jump to hit the koopa. Wait until the piranha plant goes down to jump on the pipe and go through the corridor. You'll do some more jumps and hit a section with three one block pillars and a question mark block, jump on to all three individually. Do more jumps at you'll come up to bowser. Thus, ending the run.