The correct increasing covalent character is

Covalent character in a compound is found by Fajans Rule.

(i) Greater the size of the cation, more will be the ionic character and

(ii) Greater the size of anion, more will be its covalent character and charge on the cation is dominant over the size of the cation.

(iii) Greater the charge on the cation, more will be its covalent character.

Hence   ${\mathrm{BeCl}}_2 > \mathrm{LiCl} > \mathrm{NaCl}$ (in covalent character)