Base levels, plus what each job reaches at four condensing stars (light cells). The top level is 10.
MiningLv 7 out of 10→ 10★4, Lv 10 at four condensing stars
KindlingLv 6 out of 10→ 8★4, Lv 8 at four condensing stars
Condensing raises its jobs like this:
★1 +1 Mining
★2 +1 Kindling
★3 +1 Mining
★4 +1 to every job
Condense it at a Pal Essence Condenser (unlocks at Lv 14) using 4, 8, 12 and 24 more Blazamut Ryu for each star (48 in all). Or feed it Starfruit ☆1 to ☆4 from the Medal trader, or a Ripe Starfruit from the Bounty token exchange. The Condenser shows the new levels before you confirm.
The game picks the drop list by level: a wild Blazamut Ryu at Lv 70 or higher uses the World Tree list instead of the normal one, and at Lv 80 the Aura list. World Tree farming guide
Two Blazamut Ryu always hatch another Blazamut Ryu. No other pair makes Blazamut Ryu, so you need two of it. Where to catch Blazamut Ryu. Breeding rank 100.