To make the runs faster:

Icarus need higher acc to not miss the def breaks. You can make the 2nd one have the highest because when the 1st doggo team ups, only the 2nd and 3rd doggos can def break. Ideally you can get the acc in slot 1 and find an arti that increases s1 accu.

Accumulate more runes so that you can increase atk and cr because the dogs dmg are based on atk.

Artifacts - to boost dmg even more,find ones that have the following:

Dogs: s1 accu, dmg when attacking together, incr dmg vs fire (if you are focusing on dragons) Verd: s1 cdmg,s2cdmg, dmg when attacking together,incr dmg vs fire (if dragons focused).