I need to install Internet Explorer on my MacBook Pro.

I have a MacBookPro (mid 2012) 0SX 10.8.5, Processor 2.5 GHz Intel Core i5: Memory 4 GB 1600 MHz DDR3. I need Microsoft Internet Explorer to access websites essential to my business. I need a solution that will allow me to access a portal for health plan insurers (NaviNet) and the Medicare provider website. I installed the Opera browser, reading that it can "imitate" IE, but I lack the expertise to make that work (if it can work). I would find installing "Windows for Mac" repugnant, but will do it if that is the only route. Please advise.

Elizabeth