She went to the supermarket to do some shopping.

Literal

She [topic-は] supermarket [to-へ] shopping [for-へ] went.

The double へ here is unusual — the canonical pattern would be スーパーへ買い物に行った, with へ marking the destination (the supermarket) and に marking the purpose (going for the purpose of shopping). The に for purpose attaches to a verb stem or activity noun: 買い物に行く ('go shopping'), 釣りに行く ('go fishing'), 食事に行く ('go for a meal'). The pattern reads as a likely typo or stylistic choice in the source; in standard Japanese, mix the two particles for clarity.