Ike solo runs into the same problem of most solos, which is that it's a combination of dullness (moving one units isn't very strategic) and the horribleness of that part in Ch. 17 where Ike has to carry Leanne and gets his stats halved.
Some run ideas:
No restarts
Rest run (Units must take a chapter off for every chapter they participate in)
Females only (not that hard if you can clear the early chapters with just Titania)
Bad units run (Bastion! Geoffrey! Tanith!)
No buying items (I have no clue how hard this would be, though I suppose the late-game could basically be an Ike solo)
No staves
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SubDeity wants to vote for Calvin Coolidge. [Evil Republican]
Play Der Langrisser.