$L1=\{ww \mid w \in \{a,b\}^*\}\qquad$CSL
$L2=\{ww^R \mid w \in \{a,b\}^*,w^R \text{ is the reverse of w}\}\qquad$Palindrome, so CFL
$L3=\{0^{2i} \mid i \text{ is an integer}\}\qquad$Linear power and regular expression can be stated as $(00)^*$
$L4=\{0^{i^2} \mid i \text{ is an integer}\}\qquad$Non-linear power, so CSL
Therefore, answer is option D.