ttF = Tooltip[#, "The Iliad of Homer"] &;
Use "The Iliad of Homer" as the tooltip for the nodes and the edge:
TreePlot[{ttF[# -> #2] & @@ ttF /@ {Peleus, Achiles}}, VertexLabeling -> All]
Alternatively, (1) Use the syntax $\left\{\left\{v_i\to v_j,\text{lbl}_1\right\},\ldots \right\}$ instead of $\left\{v_i\to v_j,v_{2 i}\to v_{2 j},\ldots \right\}$ to specify the edges.
(2) Use the option settings VertexLabeling -> All and EdgeLabeling -> Automatic.
(3) Post-process the TreePlot output to change the Tooltip labels.
TreePlot[{{Peleus -> Achiles, ""}}, VertexLabeling -> All, EdgeLabeling -> Automatic] /.
Tooltip[v_, _] :> Tooltip[v, "The Iliad of Homer"]
(* same picture *)