What are appropriate noncombat, nonspell feats at each tier?

[Anymage]

I'm not asking for what RAW says/implies here. Rather, if D&D characters of a given level band were characters in a movie, what sorts of impressive stuff would you expect to see them pull off other than "hit something really hard/fast" and "cast an Nth level spell". Nonphysical feats are as appreciated as physical ones - singlehandedly intimidating an army or being able to eavesdrop on a conversation on the other end of a bustling castle are at least as impressive as outrunning a horse or suplexing a train - but I'm curious what power levels and appropriate feats people would benchmark for each leveling tier.

[Ignimortis]

Well, let's go by a couple basic skills and assume that "heroic" fantasy starts from level 1...
Athletics:
Tier 1: Jump 10 feet far while wearing armor. Run+climb up a short (6-7 ft) wall and vault over it at the end. Wrestle an ogre and win.
Tier 2: Jump 10 feet high or 30 feet far, while wearing armor. Run for a day without being fatigued by the end of it. Wrestle a (huge) giant and win.
Tier 3: Jump 50+ feet high or 100+ feet far, while wearing armor (and possibly wrestling a dragon in the process). Parkour across trees in a forest without issue or slowing down, or leap a series of falling stones. Run across walls as normal movement. Suplex a train.
Tier 4: Jump up to the clouds or over mountains. Run without tiring, ever (needs a bit of a wind-up), and at speeds more akin to a car than a normal person. Wrestle anyone, really, you can outgrapple a titan.
Acrobatics:
Tier 1: Balance on a tightrope, ignore damage from falling as high as 10-12 feet. Land on your feet in most circumstances.
Tier 2: Balance on a wet, oily tightrope or snow surface. Ignore damage from falling as high as 30 feet. Land on your feet, unless you took severe damage from the fall. Never slip for mundane reasons.
Tier 3: Balance on water surface well enough to run across it. Ignore damage from falling as high as 300 feet. Always land on your feet, never slip for any reason that isn't "you got explicitly knocked down".
Tier 4: Balance on clouds, smoke, anything thicker than air. Falling damage is fiction and you have proved it so. So is slipping.
Investigation:
Tier 1: Do basic detective work, find clues or hidden objects, notice (most likely) real connections between disjointed facts.
Tier 2: Expert detective, easily find clues others might have missed, a thorough search reveals everything not hidden by powerful magic, can construct a decent theory about an issue even without possession of all proper facts.
Tier 3: Sherlock Holmes applauds you. No case can remain unsolved, and your searches can foil magic and mundane tricks alike.
Tier 4: Gods would like to talk to you about tracking down specific things. With enough time for a decent search, even the most powerful magic fails to stop you from finding anything hidden.
Intimidation:
Tier 1: Stop a tavern brawl by intimidating the toughest fighters. Subtly yet successfully imply that certain actions might threaten someone's life and loved ones much more than they anticipate.
Tier 2: Cast deep and enduring fear into hearts of people previously ready to fight. Successfully threaten anything that has an INT score. Threaten someone so successfully they actually are Frightened.
Tier 3: Stop an army by intimidating not only the commander, but everyone involved. Cause intimidated targets to flee in panic.
Tier 4: Threaten anything - your sheer aura of menace is almost palpable and goes beyond the mundane. Scare someone so hard, they drop dead on the spot. Threaten gods and have them fear you, despite everything.

Something like that.
In short, it's something like:
Tier 1: Reasonably human, if very skilled and powerful.
Tier 2: Superhuman, but mostly real things taken to 11.
Tier 3: Superhuman and it shows. Outright impossible feats, stuff of legends, something that Heracles or Beowulf might've achieved.
Tier 4: Demigod in all but name. High-end wuxia tricks, endgame JRPG protagonists.

[Psyren]

Some of this is situational which is probably why it's not codified in the text. For example, while I think a high level character intimidating an entire army into fleeing is reasonable, some DMs might require that the army in question know you or your reputation to have any chance of success, while others would be fine with you doing that purely with your personal magnetism or aura of menace even if they have no idea who you are. That divide is the kind of thing that should be left up to the DM and their world rather than prescribed as a generic rule.