I doubt these would be helpful 2 years after asking that question, but here are the direct translations of the names of areas on the Area Selection screen:

Free Area
FREE[e][ri][a]
ＦＲＥＥエリア

Nightmare Area
[na][i][to][me][a][e][ri][a]
ナイトメアエリア

Survival Area
[sa][ba][i][ba][ru][e][ri][a]
サバイバルエリア

Panic Area
[pa][ni][k][ku][e][ri][a]
パニックエリア

Infinity Area
[mu][ge][n][e][ri][a]
むげんエリア
無限エリア

Male Characters Only Area
[o][to][ko][k][ya][ra][ge][n][te][i][e][ri][a]
おとこキャラげんていエリア
男キャラ限定エリア

Female Characters Only Area
[o][n][na][k][ya][ra][ge][n][te][i][e][ri][a]
おんなキャラげんていエリア
女キャラ限定エリア

Elimination Area
[se][n][me][tsu][e][ri][a]
せんめつエリア
殲滅エリア

Showdown Area
[ta][i][ji][e][ri][a]
たいじエリア
対峙エリア

Secret Area
SECRET[e][ri][a]
ＳＥＣＲＥＴエリア

Thank you. Though I started studying Japanese last year, kanji is still not one of my strong points. Mainly '殲滅' senmetsu and '殲滅' taiji, thank you for the translation.