To run your server in one of the special modes and see it flagged as such in Battlelog, go to the "Easy setup" page and click the option to adjust settings to match that mode, and they'll be set for you (you'll also have to submit the form).
For reference, those settings are given below. If you choose a combination of settings that does not match those in any column, your server will be declared "Custom".
Setting Normal Hardcore Infantry Only
------- ------ -------- -------------
vars.playerRespawnTime 100 100 100
vars.soldierHealth 100 60 100
vars.playerManDownTime 100 100 100
vars.bulletDamage 100 100 100
vars.vehicleSpawnAllowed true true false
vars.friendlyFire false true false
vars.regenerateHealth true false false
vars.3dSpotting true false true
vars.nameTag true false true
vars.hud true false true
vars.miniMap true true true
vars.miniMapSpotting true true true
vars.killCam true false true
vars.autoBalance true true true
vars.3pCam true false false
vars.regenerateHealth true false true
vars.onlySquadLeaderSpawn false true false
Note that the "Easy setup" page also allows for a few other settings, which you can adjust to whatever you'd like.
(The information above was taken from the "Server settings and Battlelog" section of the official server administrator documentation