What net is very good at catching rare 2 star pets? I've tried a blue net like 7 times and failed..... Each rare 2 star I've tried to catch were beautiful and amazing looking to......

Masterful Traps can trap anything but they are hard to find or get.
Though Standard Traps can sometimes trap rares, They are found in the sanctuary in umbra, the seconed region. Theres also another kind of trap in Astrl's Vale, That can catch common, uncommon, rare and epic

traps, what they work on, and where to get them guide here (post 9, if images loading moves you around)

Generally speaking, unthemed blue-star pets aren't worth the trap cost required to catch them (but of course there's always gonna be the ones you just can't bear to knock out)
(and I'd have to say that you do not want to use a master snare on a blue star unless it's a themed nephini)

Lowering HP does make the chance of success more likely though we the players have no idea exactly what the calculations in that are, only Krin does