This study was conducted to examine the chemical composition of the essential oils (EOs) from six Tunisian Eucalyptus species and to evaluate their anti-enzymatic and antibiofilm activities. The EOs were obtained through hydro-distillation of dried leaves and subsequently analyzed using GC/MS. The main class of compounds was constituted by oxygenated monoterpenes, particularly prominent in E. brevifolia (75.7%), E. lehmannii (72.8%), and E. woollsiana (67%). Anti-enzymatic activities against cholinesterases, α-amylase, and α-glucosidase were evaluated using spectrophotometric methods. Notably, the E. brevifolia, E. extensa, E. leptophylla, E. patellaris, and E. woollsiana EOs displayed potent acetylcholinesterase (AChE) inhibition (IC50: 0.25–0.60 mg/mL), with E. lehmannii exhibiting lower activity (IC50: 1.2 mg/mL). E. leptophylla and E. brevifolia showed remarkable α-amylase inhibition (IC50: 0.88 mg/mL), while E. brevifolia and E. leptophylla significantly hindered α-glucosidase (IC50 < 30 mg/mL), distinguishing them from other EOs with limited effects. Additionally, the EOs were assessed for their anti-biofilm properties of Gram-positive (Staphylococcus aureus and Listeria monocytogenes) and Gram-negative (Acinetobacter baumannii, Pseudomonas aeruginosa and Escherichia coli) bacterial strains. The E. extensa EO demonstrated the main antibiofilm effect against E. coli and L. monocytogenes with an inhibition > 80% at 10 mg/mL. These findings could represent a basis for possible further use of Eucalyptus EOs in the treatment of human microbial infections and/or as a coadjutant in preventing and treating Alzheimer’s disease and/or diabetes mellitus.