gyre
The given definition is for "gyre" as a noun, but the example sentence is using it as a verb, which could connect to "gyrate" ("to wind or move in a spiral course"--often in a dance).
’Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
beware
“Beware the Jabberwock, my son!
claw
The jaws that bite, the claws that catch!
shun
Beware the Jubjub bird, and shun
The frumious Bandersnatch!
foe
Long time the manxome foe he sought—
flame
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!
through
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!
burble
"Burble" also means "babble" (which is possible because many of the animals that Alice encounters through the looking glass can talk) and "gurgle" (which is also possible because Alice found the poem in a book on the other side of the looking glass, where things often look or are backwards, so a scary monster that gurgles like a baby would not be out of place).
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!
snicker
Although the phrase "snicker-snack" sounds more onomatopoeic than meaningful, it could suggest the image of the boy laughing disrespectfully while his blade made snicker-snacking sounds through the Jabberwock's body.
The vorpal blade went snicker-snack!
galumph
He went galumphing back.
slay
“And hast thou slain the Jabberwock?
beamish
Come to my arms, my beamish boy!
chortle
He chortled in his joy.
gambol
The made-up word "gimble" sounds like the real word "gambol"--the definition fits the overall happy mood of this stanza that starts and ends a poem about the successful killing of a monster. But according to Carroll's Humpty Dumpty, "gimble" means "to make holes like a gimlet" (a gimlet is similar to a corkscrew, which the toves look like).
’Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;