All 'speedrun mode' stages completed with S-rank by me, who is not a speedrunner and almost gave up trying to get this achievement.

Super Mario Bros.:
00:00 Mushzoom (4.16)
00:24 Loose Change (1.93)
00:40 Step It Up (4.91)
00:59 ? Block Party (3.61)
01:17 Run for Your Money (3.31)
01:34 One on 1-1 (21.16)
02:11 Hit the Bricks (10.73)
02:37 Axe to Grind (15.20)
03:10 Shoo, Lakitu! (24.05)
03:50 Cash Grab (51.66)
04:55 In the Zone (25.66)
05:36 Sink or Swim (36.41)
06:25 Cheep Cheep Chase (25.26)
07:05 Mario Master (6.28.48)

The Legend of Zelda:
13:54 Don't Go Alone (7.96)
14:15 Octorok Onslaught (2.45)
14:28 Fire in the Hole (2.85)
14:42 Key of the Keese (3.28)
14:57 Take Heart (27.55)
15:37 Aquamentus Argumentus (4.50)
15:54 A secret to Everybody (7.60)
16:14 Gut Bomb (6.20)
16:32 Death Mountain Duel (6.85)
16:50 Deadeye (7.33)
17:10 Beneath the Hollow Tree (23.81)
17:46 Darknut Dustup (5.28)
18:02 Wizzrobe Warrior (6.05)
18:22 The Body Will Follow (9.28)
18:44 Labyrinth Champion (1.30.03)

Metroid:
20:31 Power Grab: Morph Ball (3.75)
20:47 Quickdraw (2.75)
21:03 Power Grab: Bomb (6.40)
21:23 Up & Out (27.55)
22:04 Power Grab: Missle (13.63)
22:30 Power Grab: Screw Attack (11.75)
22:55 Breakdown (12.85)
23:20 Kraid Raid (29.28)
24:02 Ridley Riddance (31.40)
24:46 Elevator Blitz (32.51)
25:31 Avoid the Metroids (18.51)
26:03 Escape Expert (33.48)

Donkey Kong:
26:52 Bottom Rung (4.93)
27:11 Hammer Hustle (10.75)
27:34 Barrel Roll (21.40)
28:07 Lost & Found (12.60)
28:30 Jumping Jacks (14.85)
28:57 Finders Keepers (16.11)
29:25 Construction Destruction (30.50)
30:09 Kong Crusher (1.32.48)

Kid Icarus:
31:57 Seek & Destroy (7.38)
32:17 Pitcher Perfect (8.06)
32:39 Spa Treatment (5.45)
32:57 Harp on It (24.21)
33:37 Specknose Spectacle (9.70)
33:59 Water Divination (14.21)
34:27 Overcome the Underworld (1.18.48)
36:00 Eggplant Harm (12.38)
36:25 Underworld Wonder (2.6.43)

Super Mario Bros. 2 (USA):
38:46 Door to Door (5.96)
39:05 Veggie Plucking (1.11)
39:17 Sub-Space Exploration (3.96)
39:32 Leap to the Peak (6.65)
39:49 Egg Toss (17.66)
40:18 Desert Dash (19.28)
40:51 Over & Out (19.08)
41:22 Evasion is Key (20.95)
41:55 Destroyer of Dreams (19.11)
42:26 Cloudtop Climb (15.88)
42:52 Whale of a Time (16.91)
43:22 1-1 Dream Run (1.16.76)

Excitebike:
44:54 Cool It (10.48)
45:16 Heating Up (30.51)
45:59 In Rythm (30.81)
46:41 Poppin' Wheelies (33.26)
47:26 Xtreme Terrain (35.81)
48:14 Motocross Maestro (1.10.15)

Ice Climber:
49:38 Shivery Start (1.55)
49:50 Arctic Ascent (8.36)
50:11 Bonus or Bust (9.00)
50:33 Every Last Eggplant (10.63)
50:54 Peak Performance (11.28)
51:18 Condor Conqueror (38.08)

Balloon Fight:
52:10 Pop It (1.48)
52:24 Balloon Bopper (3.88)
52:40 Pop 'Em (4.28)
52:55 Balloon Burster (10.60)
53:18 Pop 'Em All (18.20)
53:49 Balloon Basher (10.33)
54:11 Ace Balloonist (36.30)

Super Mario Bros. 3:
55:00 Mushzoom 2 (2.86)
55:14 Coin Collector (2.28)
55:29 Super Leaf in the Wind (4.78)
55:45 Hammer Bro KO (3.30)
56:01 Half-Pipe (2.15)
56:16 Lookie, Tanooki! (3.53)
56:31 1-1 of a Kind (19.80)
57:02 Check 1-2 (19.85)
57:34 Ka-Boom Boom (9.26)
57:55 Curtain Call: Larry (9.83)
58:16 Beat the Heat (20.00)
58:49 Curtain Call: Morton (10.33)
59:11 Froggy Paddle (25.78)
59:49 Curtain Call: Wendy (10.30)
1:00:12 The Big Race (20.93)
1:00:45 Curtain Call: Iggy (9.76)
1:01:07 Quickstep (35.48)
1:01:54 Rotary Rush (19.68)
1:02:27 Curtain Call: Roy (9.16)
1:02:47 Hammer It Out (29.16)
1:03:30 Curtain Call: Lemmy (10.10)
1:03:52 Perilous Plants (12.20)
1:04:16 Curtain Call: Ludwig (10.00)
1:04:39 World 1 Wizard (4.59.23)

Zelda 2 - The Adventure of Link:
1:09:54 Monster Slayer (3.93)
1:10:11 Leveling Up (3.65)
1:10:27 Fairy Finder (1.28)
1:10:42 Cliff Jumping (11.56)
1:11:06 Low-key Hero (20.60)
1:11:38 No Bones About It (4.68)
1:11:56 Goodbye, Guma (8.23)
1:12:18 Crumbling Crossing (11.48)
1:12:45 Knuckle Sandwich (7.28)
1:13:05 Magic Jar Excavation (4.98)
1:13:22 Neigh Slayer (15.03)
1:13:51 Rebonack Attack (18.86)
1:14:23 Rescue Operation (18.68)
1:14:54 Firefight (3.56)
1:15:13 Parapa Palace Pro (3.35.95)

Super Mario Bros. 2 (JP):
1:19:05 Not Lichen It (4.26)
1:19:20 Paratroopa Toppling (1.43)
1:19:34 Mushzoom 3 (4.48)
1:19:50 Staircase Race (5.38)
1:20:08 Mario vs. 1-1 (26.05)
1:20:46 Luigi vs. 1-1 (26.50)
1:21:24 Divemaster (38.93)
1:22:17 Lost Legend (28.65)

Kirby's Adventure:
1:22:59 Inhale without Fail (3.21)
1:23:14 Taking Flight (3.95)
1:23:30 Quick Copy (1.88)
1:23:45 Updraft (5.38)
1:24:03 Exit Stage Right (12.53)
1:24:29 Bombs Away (6.70)
1:24:48 Walloping Whispy Woods (20.50)
1:25:20 Coconut Rush (11.66)
1:25:45 Busting Up Bonkers (12.66)
1:26:10 New Heights (24.01)
1:26:47 Fireball Rush (19.35)
1:27:19 Meta-Knights Strike (14.56)
1:27:47 1-1 and Done (36.93)
1:28:37 Unidentified Flying Kirby (27.35)
1:29:17 Favorable Wind (30.58)
1:30:01 Eye in the Sky (18.63)
1:30:32 Wheels Down (15.78)
1:31:01 Shipshape (17.10)
1:31:30 Meta Knight Sword Fight (27.83)
1:32:11 Monochrome Hero (1.39.00)