"shyer" or "shier"
Solution 1:
"shyer" or "shier"?
Both versions are acceptable in today's standard English.
In the 2002 CGEL page 1581:
Monosyllabic dry and shy are optionally exceptions to the y-replacement rule, allowing either y or i before the suffix: dry ~ dryer/drier ~ dryest/driest and shy ~ shyer/shier ~ shyest/shiest.
Note that CGEL is the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL).