You do need more healers. You also need a larger roster of level 60 characters to use.
GW is meant to be a long term goal for most players. You're not meant to be able to clear the whole board as soon as you hit 60.
Having said all that though, it's very odd that you're getting level 60 teams in only the second fight. Usually you're meant to start off with a few easier low level AI groups before you start hitting the more difficult player groups.
Are you consistently getting level 60 teams like this on the 2nd/3rd battle? Or was this a once off scenario?
Maybe @EA_Jesse can shed some light on this for you? Could be a potential bug?
