This is a playthrough of every stage in the No Flickies Romhack, which provides a decent look at how an average player would fare at completing the time challenges quickly (Without Super Sonic). Also, this is not my video or content.
Here are the times that this player got for each stage:
Green Grove Act 1: 0:26
Green Grove Act 2: 0:49
Green Grove Boss: 0:29
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Rusty Ruins Act 1: 1:08
Rusty Ruins Act 2: 1:20
Rusty Ruins Boss: 0:26
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Spring Stadium Act 1: 1:04
Spring Stadium Act 2: 1:31
Spring Stadium Boss: 0:37
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Diamond Dust Act 1: 1:24
Diamond Dust Act 2: 1:08
Diamond Dust Boss: 0:56
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Volcano Valley Act 1: 1:24
Volcano Valley Act 2: 0:45
Volcano Valley Boss: 0:20
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Gene Gadget Act 1: 1:09
Gene Gadget Act 2: 0:35
Gene Gadget Boss: 1:19
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Panic Puppet Act 1: 0:55
Panic Puppet Act 2: 1:12
Panic Puppet Boss: 1:50
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Final Fight: 3:52