Here's the solution:
1. Take two magics and refreshment.
2. Use WONAFYT, but don't kill Beagle. Make sure WONAFYT doesn't put him on he altar.
3. Use BYCEPS.
4. Convert BYCEPS and cast ENDISWALL.
5. Hit Sir Mutton.
6. Convert ENDISWALL.
7. Cast WEYTWUT in Lord Mutton.
8. Convert WONAFYT.
9. Take Flames, Fireball Lord Mutton, and kill Beagle so the burning takes out his DP.
10. Convert WEYTWUT and fireball Lord Mutton
Darn, I got ninja'd.