One thing's for sure: the speaker of this poem is clearly not Abraham Lincoln. We're quite sure he wouldn't be so dismissive of turtles. The speaker's scornful tone in the poem's opening line hints that this turtle will probably have to swim against the current, persevering on her own without the benefit of an outboard motor or vigilant lifeguards.
[…] barely mobile (2)
If you're a marathon runner, perseverance is your middle name. You've trained your body well for long-distance running and have confidence in your powers of endurance. The turtle, however, is "barely mobile." In the race of life, she will always remain slow and awkward, and no amount of training will change that fact. Yet she perseveres.
[…] almost any slope Defeats her modest hopes (6-7)
Many expert mountain climbers who attempt Everest have to turn back; but there's no shame in being defeated by the world's tallest mountain. They can still point to their conquests of other impressive peaks. The turtle doesn't have any record to fall back on, no history of successes to keep her going. No wonder her hopes are "modest." In fact, it's a miracle that she has any hope at all. But the girl just digs deep and keeps on truckin'.
Her only levity is patience (14)
Grown-ups are always telling little kids to be patient. Often, it means waiting, but sometimes it means persevering: for example, trudging through the mall with your mom when you're tired and cranky and jealous of your baby brother who gets to ride in the stroller. "Perseverance" is one synonym of "patience." But the link to lightheartedness is unclear. The turtle is no Energizer Bunny, so what's with the levity? Must be a private joke. Turtle's got a secret. And apparently it's what keeps her going.