。
She is firmly resolved to have her own shop.
Literal
She [topic-は] her own shop [object-を] have-let's [intent-と] firmly mind [in-に] is-deciding.
~ようと + 心に決める is the set frame for 'resolve to do X' — the volitional ~ようと marks the intended action, と quotes that intention, and 心に決める ('to fix in one's mind') stamps it as a firm resolution. 堅く ('firmly, hard, unyielding') intensifies the resolution. With ~ている, 決めている is the resultative state — 'has made up her mind' (and is in that resolved state). 持とう is the volitional of 持つ ('to have, hold, own'); having one's own shop is a classic small-business aspiration.