If the top is particleboard replace it. DO NOT tile over the particle board. Replace the top with 3/4" ACX plywood, overlay the plywood with 1/4"hardie backer or similar in thin set mortar and lay your tile. This is the prefered method. You can omit the hardie backer, but the few extra $$ are worth it.
You can tile over the Formica provided the top is sound, there are no air pockets under it, the seams are tight and even, and the top is smooth not textured. You need to belt sand the top with a 24 or 36 grit belt (use 3m purple), put a crosshatched pattern XXXXXX on the top until the shine is gone, do not sand thru the top. Hand sand the edges where the belt sander will not reach. You can put Formica over Formica with this method.
What ever method you choose Use thin set mortar with a laxex additive, not mastic.
If you tear up the Formica be very careful as broken edges are razor sharp. You need to pull the sink out anyway, I'd replace the whole top with plywood, glue and nail a 3/4 X 1 1/4 all along the front edge of the plywood to support your bullnose tile.