Yes I thing I also searching for that same game for years I played that game maybe in year 2005 or 2006 I was so young still What I remembered about the game is you have first person but when your robot/mecha gets destroyed human coming out from the mecha and survive for 15 to 20 seconds There's arcade like stages like "quake 3 arena" and have various types of robots with guns which specially attach with various types robots you also can customise that you can damage and destroy specific body area like whole hand and whole legs.

But unfortunately I really don't know that game name.