...が...を...みせる => make it look like... N4
Base, base
てみせる => I'll show you ~ N4
Purpose, target
...を...みる => judging from; seeing that ~ N4
Deduce
姿を見せる => figure; appearance N3
Ability
てみせる => To show (the action) A N1
Will, Decision, Doing
... ところをみると => judging from; seeing that ~ N3
Speculation
ようにみせる => to look; to seem; to appear ~ N4
Consider it
てみせる  => I’ll do my best; I'll definitely do; I'll show you N2
Determined, determined
てすみません => I'm sorry for... N4
NがNを/にV-させる => Who (N) makes...who (N) do what N4
Coercion
をして…させる => to make somebody do something, to let somebody do something N2
Allow
てみる => try doing ~ N4
Evaluate