I assume you mean at or under 40 BP, but please specify. Also, the required STAB move can be of any BP? And by map tiles, do you mean riles that cover the entire screen?Espeon, take a male Nidoran. He may know one STAB move and one move at or over 40BP (not including STAB). He may know at most two damaging moves, and may never hold an item.
To unlock evolution, additional damaging moves, and higher BP totals, you must earn and spend points, according to the following charts:
Challenge (points gained):
Solo all gym trainers (1)
Solo a gym leader (1)
Solo any of the above with a type disadvantage (+1)
Solo a rival battle (1)
Solo a short (1-3 map tiles) route from start to finish (1)
Solo a long (4+ map tiles) route from start to finish (2)
Solo a dungeon (cave, forest etc.) from start to finish (2)
Solo a route/dungeon without repels or fleeing (+1)
Solo any of the above without healing items (+1)
Faint while attempting any of the above (-1)
Yes, you can go into negative points. If you do, it won't cost you the upgrades you have already, but it makes it tougher to get new ones
Unlocked (points cost)[max times to buy]:
+10 BP for all moves (1)
+1 damaging moveslot (1)
+1 evolutionary stage (3)
+1 move over BP limit (2)
+ability to hold item (2)
Note: Route solos include all trainers on the route, and may only be attempted the first time you pass through that route. If you return through a route later, you do not have to continue soloing it. If you faint during a route solo, you may not continue it, and you must take the -1 point.
Any other questions, feel free to ask.