A documented Defender of the Crown no loss run. (Goal: level 30)

[Fatt_Shade]

Other then 2nd lvl pet dragon, there is no other conditions for pet digging skill. You can get it on 2nd lvl (since first lvl is always push hit), and 2nd lvl of digging you can get on 3rd lvl pet dragon. In ga,e folder/Kings Bounty Armored princess/sessions/defender/defender.kfs check pet.atom file, there are all pet dragon skills and condition.
Expl :

smash_hit {
ad_factor=0
class=scripted
script_calccells=calccells_smash_hit
script_attack=pet_smash_hit
attack_cursor=attack
place=1
level=1
default=level1
upgrade {
level1=level:0/damage:physical:90:100,rage:4,rest:1,exp:3,push:1, level:1
level2=level:1/damage:physical:130:150,rage:+1,exp:+2,level:2
level3=level:2/damage:physical:200:300,rage:+2,exp:+3,level:3
level4=level:3/damage:physical:400:500,rage:+3,exp:+5,push:+1,lev el:4
level5=level:4,LV:>9/damage:physical:800:900,rage:+4,exp:+6,level:5
level6=level:5,LV:>13/damage:physical:1300:1400,rage:+5,exp:+7,level:6
level7=level:6,LV:>17/damage:physical:1900:2000,rage:+6,exp:+8,rest:+1, rage1=level:>0,rs:0,rage:>18/rage:-5,rs:1
rest1=level:>0,rr:0,rest:>1/rest:-1,rr:1
}

place=1 is location of skill, first slot in first row.

level=1 is condition pet dragon need to have chance to get this skill on lvlup.

level3=level:2/damage:physical:200:300,rage:+2,exp:+3,level:3 for level3 you need level:2 of this skill (obviously ) and it upgrades dmg

level5=level:4,LV:>9/damage:physical:800:900,rage:+4,exp:+6,level:5 but for level5 of this skill, you need it upgraded to lvl:4 AND pet dragon LV>9 higher then 9lvl.

So this skill have conditions to upgrade to lvl 5+.
Digging on other hand have no conditions for pet lvl.